WorldWideScience

Sample records for graph theoretic algorithms

  1. Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms

    Directory of Open Access Journals (Sweden)

    Furmańczyk Hanna

    2016-09-01

    Full Text Available In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.

  2. Planar graphs theory and algorithms

    CERN Document Server

    Nishizeki, T

    1988-01-01

    Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.

  3. MultiAspect Graphs: Algebraic Representation and Algorithms

    Directory of Open Access Journals (Sweden)

    Klaus Wehmuth

    2016-12-01

    Full Text Available We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs. A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS, and Depth First Search (DFS. These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.

  4. Extracting Gene Networks for Low-Dose Radiation Using Graph Theoretical Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Voy, Brynn H [ORNL; Scharff, Jon [University of Tennessee, Knoxville (UTK); Perkins, Andy [University of Tennessee, Knoxville (UTK); Saxton, Arnold [University of Tennessee, Knoxville (UTK); Borate, Bhavesh [University of Tennessee, Knoxville (UTK); Chesler, Elissa J [ORNL; Branstetter, Lisa R [ORNL; Langston, Michael A [University of Tennessee, Knoxville (UTK)

    2006-01-01

    Genes with common functions often exhibit correlated expression levels, which can be used to identify sets of interacting genes from microarray data. Microarrays typically measure expression across genomic space, creating a massive matrix of co-expression that must be mined to extract only the most relevant gene interactions. We describe a graph theoretical approach to extracting co-expressed sets of genes, based on the computation of cliques. Unlike the results of traditional clustering algorithms, cliques are not disjoint and allow genes to be assigned to multiple sets of interacting partners, consistent with biological reality. A graph is created by thresholding the correlation matrix to include only the correlations most likely to signify functional relationships. Cliques computed from the graph correspond to sets of genes for which significant edges are present between all members of the set, representing potential members of common or interacting pathways. Clique membership can be used to infer function about poorly annotated genes, based on the known functions of better-annotated genes with which they share clique membership (i.e., ''guilt-by-association''). We illustrate our method by applying it to microarray data collected from the spleens of mice exposed to low-dose ionizing radiation. Differential analysis is used to identify sets of genes whose interactions are impacted by radiation exposure. The correlation graph is also queried independently of clique to extract edges that are impacted by radiation. We present several examples of multiple gene interactions that are altered by radiation exposure and thus represent potential molecular pathways that mediate the radiation response.

  5. Extracting gene networks for low-dose radiation using graph theoretical algorithms.

    Directory of Open Access Journals (Sweden)

    Brynn H Voy

    2006-07-01

    Full Text Available Genes with common functions often exhibit correlated expression levels, which can be used to identify sets of interacting genes from microarray data. Microarrays typically measure expression across genomic space, creating a massive matrix of co-expression that must be mined to extract only the most relevant gene interactions. We describe a graph theoretical approach to extracting co-expressed sets of genes, based on the computation of cliques. Unlike the results of traditional clustering algorithms, cliques are not disjoint and allow genes to be assigned to multiple sets of interacting partners, consistent with biological reality. A graph is created by thresholding the correlation matrix to include only the correlations most likely to signify functional relationships. Cliques computed from the graph correspond to sets of genes for which significant edges are present between all members of the set, representing potential members of common or interacting pathways. Clique membership can be used to infer function about poorly annotated genes, based on the known functions of better-annotated genes with which they share clique membership (i.e., "guilt-by-association". We illustrate our method by applying it to microarray data collected from the spleens of mice exposed to low-dose ionizing radiation. Differential analysis is used to identify sets of genes whose interactions are impacted by radiation exposure. The correlation graph is also queried independently of clique to extract edges that are impacted by radiation. We present several examples of multiple gene interactions that are altered by radiation exposure and thus represent potential molecular pathways that mediate the radiation response.

  6. Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models

    Directory of Open Access Journals (Sweden)

    Tomasz Kajdanowicz

    2016-09-01

    Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

  7. Graph Colouring Algorithms

    DEFF Research Database (Denmark)

    Husfeldt, Thore

    2015-01-01

    This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...

  8. Algorithms for Planar Graphs and Graphs in Metric Spaces

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...

  9. Gems of combinatorial optimization and graph algorithms

    CERN Document Server

    Skutella, Martin; Stiller, Sebastian; Wagner, Dorothea

    2015-01-01

    Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory?  Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student seminar?  Or perhaps you just want an enjoyable look at some beautiful mathematical and algorithmic results, ideas, proofs, concepts, and techniques in discrete mathematics and theoretical computer science?   Gems of Combinatorial Optimization and Graph Algorithms is a handpicked collection of up-to-date articles, carefully prepared by a select group of international experts, who have contributed some of their most mathematically or algorithmically elegant ideas.  Topics include longest tours and Steiner trees in geometric spaces, cartograms, resource buying games, congestion games, selfish routing, revenue equivalence and shortest paths, scheduling, linear structures in graphs, contraction hierarchies, budgeted matching problems, and motifs in networks.   This ...

  10. A cluster algorithm for graphs

    NARCIS (Netherlands)

    S. van Dongen

    2000-01-01

    textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)

  11. Discrete geometric analysis of message passing algorithm on graphs

    Science.gov (United States)

    Watanabe, Yusuke

    2010-04-01

    We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

  12. A new cluster algorithm for graphs

    NARCIS (Netherlands)

    S. van Dongen

    1998-01-01

    textabstractA new cluster algorithm for graphs called the emph{Markov Cluster algorithm ($MCL$ algorithm) is introduced. The graphs may be both weighted (with nonnegative weight) and directed. Let~$G$~be such a graph. The $MCL$ algorithm simulates flow in $G$ by first identifying $G$ in a

  13. Graph Algorithm Animation with Grrr

    OpenAIRE

    Rodgers, Peter; Vidal, Natalia

    2000-01-01

    We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...

  14. Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

    KAUST Repository

    Zenil, Hector

    2018-02-24

    We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumeration all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity---both theoretical and numerical---with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.

  15. Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

    KAUST Repository

    Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

    2018-01-01

    We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumeration all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity---both theoretical and numerical---with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.

  16. BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.

    Science.gov (United States)

    Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter

    2013-02-01

    Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of

  17. Graph algorithms in the titan toolkit.

    Energy Technology Data Exchange (ETDEWEB)

    McLendon, William Clarence, III; Wylie, Brian Neil

    2009-10-01

    Graph algorithms are a key component in a wide variety of intelligence analysis activities. The Graph-Based Informatics for Non-Proliferation and Counter-Terrorism project addresses the critical need of making these graph algorithms accessible to Sandia analysts in a manner that is both intuitive and effective. Specifically we describe the design and implementation of an open source toolkit for doing graph analysis, informatics, and visualization that provides Sandia with novel analysis capability for non-proliferation and counter-terrorism.

  18. Graph Theoretical Analysis Reveals: Women's Brains Are Better Connected than Men's.

    Directory of Open Access Journals (Sweden)

    Balázs Szalkai

    Full Text Available Deep graph-theoretic ideas in the context with the graph of the World Wide Web led to the definition of Google's PageRank and the subsequent rise of the most popular search engine to date. Brain graphs, or connectomes, are being widely explored today. We believe that non-trivial graph theoretic concepts, similarly as it happened in the case of the World Wide Web, will lead to discoveries enlightening the structural and also the functional details of the animal and human brains. When scientists examine large networks of tens or hundreds of millions of vertices, only fast algorithms can be applied because of the size constraints. In the case of diffusion MRI-based structural human brain imaging, the effective vertex number of the connectomes, or brain graphs derived from the data is on the scale of several hundred today. That size facilitates applying strict mathematical graph algorithms even for some hard-to-compute (or NP-hard quantities like vertex cover or balanced minimum cut. In the present work we have examined brain graphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural brain graphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weighs less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. It is known that the female brain has a smaller gray matter/white matter ratio than males, that is, a larger white matter/gray matter ratio than the brain of males; this observation is in line with our findings concerning the number of edges, since the white matter consists of myelinated axons, which, in turn, roughly correspond to the connections

  19. A Comparative Study of Theoretical Graph Models for Characterizing Structural Networks of Human Brain

    Directory of Open Access Journals (Sweden)

    Xiaojin Li

    2013-01-01

    Full Text Available Previous studies have investigated both structural and functional brain networks via graph-theoretical methods. However, there is an important issue that has not been adequately discussed before: what is the optimal theoretical graph model for describing the structural networks of human brain? In this paper, we perform a comparative study to address this problem. Firstly, large-scale cortical regions of interest (ROIs are localized by recently developed and validated brain reference system named Dense Individualized Common Connectivity-based Cortical Landmarks (DICCCOL to address the limitations in the identification of the brain network ROIs in previous studies. Then, we construct structural brain networks based on diffusion tensor imaging (DTI data. Afterwards, the global and local graph properties of the constructed structural brain networks are measured using the state-of-the-art graph analysis algorithms and tools and are further compared with seven popular theoretical graph models. In addition, we compare the topological properties between two graph models, namely, stickiness-index-based model (STICKY and scale-free gene duplication model (SF-GD, that have higher similarity with the real structural brain networks in terms of global and local graph properties. Our experimental results suggest that among the seven theoretical graph models compared in this study, STICKY and SF-GD models have better performances in characterizing the structural human brain network.

  20. Optimizing graph algorithms on pregel-like systems

    KAUST Repository

    Salihoglu, Semih

    2014-03-01

    We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high communication or computation cost, typically due to structural properties of the input graphs such as large diameters or skew in component sizes. We describe several optimization techniques to address these inefficiencies. Our most general technique is based on the idea of performing some serial computation on a tiny fraction of the input graph, complementing Pregel\\'s vertex-centric parallelism. We base our study on thorough implementations of several fundamental graph algorithms, some of which have, to the best of our knowledge, not been implemented on Pregel-like systems before. The algorithms and optimizations we describe are fully implemented in our open-source Pregel implementation. We present detailed experiments showing that our optimization techniques improve runtime significantly on a variety of very large graph datasets.

  1. Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination

    Science.gov (United States)

    Rudinger, Kenneth Michael

    This thesis explores several theoretical questions pertaining to quantum computing. First we examine several questions regarding multi-particle quantum random walk-based algorithms for the graph isomorphism problem. We find that there exists a non-trivial difference between continuous-time walks of one and two non-interacting particles as compared to non-interacting walks of three or more particles, in that the latter are able to distinguish many strongly regular graphs (SRGs), a class of graphs with many graph pairs that are difficult to distinguish. We demonstrate analytically where this distinguishing power comes from, and we show numerically that three-particle and four-particle non-interacting continuous-time walks can distinguish many pairs of strongly regular graphs. We additionally show that this distinguishing power, while it grows with particle number, is bounded, so that no continuous-time non-interacting walk of fixed particle number can distinguish all strongly regular graphs. We then investigate the relationship between continuous-time and discrete-time walks, in the context of the graph isomorphism problem. While it has been previously demonstrated numerically that discrete-time walks of non-interacting particles can distinguish some SRGs, we demonstrate where this distinguishing power comes from. We also show that while no continuous-time non-interacting walk of fixed particle number can distinguish SRGs, it remains a possibility that such a discrete-time walk could, leaving open the possibility of a non-trivial difference between discrete-time and continuous-time walks. The last piece of our work on graph isomorphism examines limitations on certain kinds of continuous-time walk-based algorithms for distinguishing graphs. We show that a very general class of continuous-time walk algorithms, with a broad class of allowable interactions, cannot distinguish all graphs. We next consider a previously-proposed quantum adiabatic algorithm for computing the

  2. Graph-theoretical concepts and physicochemical data

    Directory of Open Access Journals (Sweden)

    Lionello Pogliani

    2003-02-01

    Full Text Available Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these types of graphs a set of graph-theoretical basis indices, the molecular connectivity indices, can be derived and used to model properties and activities of molecules. With the aid of the molecular connectivity basis indices it is then possible to build higher-order descriptors. The problem of 'graph' encoding the contribution of the inner-core electrons of heteroatoms can here be solved with the aid of odd complete graphs, Kp-(p-odd. The use of these graph tools allow to draw an optimal modeling of the molecular polarizabilities and a satisfactory modeling of the induced dipole moment of a wide set of organic derivatives.

  3. Calculating Graph Algorithms for Dominance and Shortest Path

    DEFF Research Database (Denmark)

    Sergey, Ilya; Midtgaard, Jan; Clarke, Dave

    2012-01-01

    We calculate two iterative, polynomial-time graph algorithms from the literature: a dominance algorithm and an algorithm for the single-source shortest path problem. Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point...... expressing all finite paths through a directed graph and (2) Galois connections that capture dominance and path length. The approach illustrates that reasoning in the style of fixed-point calculus extends gracefully to the domain of graph algorithms. We thereby bridge common practice from the school...... of program calculation with common practice from the school of static program analysis, and build a novel view on iterative graph algorithms as instances of abstract interpretation...

  4. Optimizing graph algorithms on pregel-like systems

    KAUST Repository

    Salihoglu, Semih; Widom, Jennifer

    2014-01-01

    We study the problem of implementing graph algorithms efficiently on Pregel-like systems, which can be surprisingly challenging. Standard graph algorithms in this setting can incur unnecessary inefficiencies such as slow convergence or high

  5. Approximate Computing Techniques for Iterative Graph Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Panyala, Ajay R.; Subasi, Omer; Halappanavar, Mahantesh; Kalyanaraman, Anantharaman; Chavarria Miranda, Daniel G.; Krishnamoorthy, Sriram

    2017-12-18

    Approximate computing enables processing of large-scale graphs by trading off quality for performance. Approximate computing techniques have become critical not only due to the emergence of parallel architectures but also the availability of large scale datasets enabling data-driven discovery. Using two prototypical graph algorithms, PageRank and community detection, we present several approximate computing heuristics to scale the performance with minimal loss of accuracy. We present several heuristics including loop perforation, data caching, incomplete graph coloring and synchronization, and evaluate their efficiency. We demonstrate performance improvements of up to 83% for PageRank and up to 450x for community detection, with low impact of accuracy for both the algorithms. We expect the proposed approximate techniques will enable scalable graph analytics on data of importance to several applications in science and their subsequent adoption to scale similar graph algorithms.

  6. Graph-theoretic techniques for web content mining

    CERN Document Server

    Schenker, Adam; Bunke, Horst; Last, Mark

    2005-01-01

    This book describes exciting new opportunities for utilizing robust graph representations of data with common machine learning algorithms. Graphs can model additional information which is often not present in commonly used data representations, such as vectors.

  7. Betweenness-based algorithm for a partition scale-free graph

    International Nuclear Information System (INIS)

    Zhang Bai-Da; Wu Jun-Jie; Zhou Jing; Tang Yu-Hua

    2011-01-01

    Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom—up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top—down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches. (interdisciplinary physics and related areas of science and technology)

  8. Exact parallel maximum clique algorithm for general and protein graphs.

    Science.gov (United States)

    Depolli, Matjaž; Konc, Janez; Rozman, Kati; Trobec, Roman; Janežič, Dušanka

    2013-09-23

    A new exact parallel maximum clique algorithm MaxCliquePara, which finds the maximum clique (the fully connected subgraph) in undirected general and protein graphs, is presented. First, a new branch and bound algorithm for finding a maximum clique on a single computer core, which builds on ideas presented in two published state of the art sequential algorithms is implemented. The new sequential MaxCliqueSeq algorithm is faster than the reference algorithms on both DIMACS benchmark graphs as well as on protein-derived product graphs used for protein structural comparisons. Next, the MaxCliqueSeq algorithm is parallelized by splitting the branch-and-bound search tree to multiple cores, resulting in MaxCliquePara algorithm. The ability to exploit all cores efficiently makes the new parallel MaxCliquePara algorithm markedly superior to other tested algorithms. On a 12-core computer, the parallelization provides up to 2 orders of magnitude faster execution on the large DIMACS benchmark graphs and up to an order of magnitude faster execution on protein product graphs. The algorithms are freely accessible on http://commsys.ijs.si/~matjaz/maxclique.

  9. Unsupervised active learning based on hierarchical graph-theoretic clustering.

    Science.gov (United States)

    Hu, Weiming; Hu, Wei; Xie, Nianhua; Maybank, Steve

    2009-10-01

    Most existing active learning approaches are supervised. Supervised active learning has the following problems: inefficiency in dealing with the semantic gap between the distribution of samples in the feature space and their labels, lack of ability in selecting new samples that belong to new categories that have not yet appeared in the training samples, and lack of adaptability to changes in the semantic interpretation of sample categories. To tackle these problems, we propose an unsupervised active learning framework based on hierarchical graph-theoretic clustering. In the framework, two promising graph-theoretic clustering algorithms, namely, dominant-set clustering and spectral clustering, are combined in a hierarchical fashion. Our framework has some advantages, such as ease of implementation, flexibility in architecture, and adaptability to changes in the labeling. Evaluations on data sets for network intrusion detection, image classification, and video classification have demonstrated that our active learning framework can effectively reduce the workload of manual classification while maintaining a high accuracy of automatic classification. It is shown that, overall, our framework outperforms the support-vector-machine-based supervised active learning, particularly in terms of dealing much more efficiently with new samples whose categories have not yet appeared in the training samples.

  10. Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs

    KAUST Repository

    Jamour, Fuad Tarek

    2017-10-17

    Betweenness centrality quantifies the importance of nodes in a graph in many applications, including network analysis, community detection and identification of influential users. Typically, graphs in such applications evolve over time. Thus, the computation of betweenness centrality should be performed incrementally. This is challenging because updating even a single edge may trigger the computation of all-pairs shortest paths in the entire graph. Existing approaches cannot scale to large graphs: they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving graphs. We decompose the graph into biconnected components and prove that processing can be localized within the affected components. iCentral is the first algorithm to support incremental betweeness centrality computation within a graph component. This is done efficiently, in linear space; consequently, iCentral scales to large graphs. We demonstrate with real datasets that the serial implementation of iCentral is up to 3.7 times faster than existing serial methods. Our parallel implementation that scales to large graphs, is an order of magnitude faster than the state-of-the-art parallel algorithm, while using an order of magnitude less computational resources.

  11. Jointly-check iterative decoding algorithm for quantum sparse graph codes

    International Nuclear Information System (INIS)

    Jun-Hu, Shao; Bao-Ming, Bai; Wei, Lin; Lin, Zhou

    2010-01-01

    For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement. (general)

  12. Scalable force directed graph layout algorithms using fast multipole methods

    KAUST Repository

    Yunis, Enas Abdulrahman

    2012-06-01

    We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach to graph layout that treats the vertices V as repelling charged particles with the edges E connecting them acting as springs. Traditionally, the amount of work required in applying the Force-Directed Graph Layout algorithm is O(|V|2 + |E|) using direct calculations and O(|V| log |V| + |E|) using truncation, filtering, and/or multi-level techniques. Correct application of the Fast Multipole Method allows us to maintain a lower complexity of O(|V| + |E|) while regaining most of the precision lost in other techniques. Solving layout problems for truly large graphs with millions of vertices still requires a scalable algorithm and implementation. We have been able to leverage the scalability and architectural adaptability of the ExaFMM library to create a Force-Directed Graph Layout implementation that runs efficiently on distributed multicore and multi-GPU architectures. © 2012 IEEE.

  13. Scalable force directed graph layout algorithms using fast multipole methods

    KAUST Repository

    Yunis, Enas Abdulrahman; Yokota, Rio; Ahmadia, Aron

    2012-01-01

    We present an extension to ExaFMM, a Fast Multipole Method library, as a generalized approach for fast and scalable execution of the Force-Directed Graph Layout algorithm. The Force-Directed Graph Layout algorithm is a physics-based approach

  14. Topological properties of the limited penetrable horizontal visibility graph family

    Science.gov (United States)

    Wang, Minggang; Vilela, André L. M.; Du, Ruijin; Zhao, Longfeng; Dong, Gaogao; Tian, Lixin; Stanley, H. Eugene

    2018-05-01

    The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.

  15. Parallel Algorithms for Graph Optimization using Tree Decompositions

    Energy Technology Data Exchange (ETDEWEB)

    Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL; Groer, Christopher S [ORNL

    2012-06-01

    Although many $\\cal{NP}$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.

  16. Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data

    OpenAIRE

    Gallant, Andrew; Leiserson, Mark DM; Kachalov, Maxim; Cowen, Lenore J; Hescott, Benjamin J

    2013-01-01

    Background New technology has resulted in high-throughput screens for pairwise genetic interactions in yeast and other model organisms. For each pair in a collection of non-essential genes, an epistasis score is obtained, representing how much sicker (or healthier) the double-knockout organism will be compared to what would be expected from the sickness of the component single knockouts. Recent algorithmic work has identified graph-theoretic patterns in this data that can indicate functional ...

  17. Generalized connectivity of graphs

    CERN Document Server

    Li, Xueliang

    2016-01-01

    Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

  18. Multifractal analysis of multiparticle emission data in the framework of visibility graph and sandbox algorithm

    Science.gov (United States)

    Mali, P.; Manna, S. K.; Mukhopadhyay, A.; Haldar, P. K.; Singh, G.

    2018-03-01

    Multiparticle emission data in nucleus-nucleus collisions are studied in a graph theoretical approach. The sandbox algorithm used to analyze complex networks is employed to characterize the multifractal properties of the visibility graphs associated with the pseudorapidity distribution of charged particles produced in high-energy heavy-ion collisions. Experimental data on 28Si+Ag/Br interaction at laboratory energy Elab = 14 . 5 A GeV, and 16O+Ag/Br and 32S+Ag/Br interactions both at Elab = 200 A GeV, are used in this analysis. We observe a scale free nature of the degree distributions of the visibility and horizontal visibility graphs associated with the event-wise pseudorapidity distributions. Equivalent event samples simulated by ultra-relativistic quantum molecular dynamics, produce degree distributions that are almost identical to the respective experiment. However, the multifractal variables obtained by using sandbox algorithm for the experiment to some extent differ from the respective simulated results.

  19. A general algorithm for distributing information in a graph

    OpenAIRE

    Aji, Srinivas M.; McEliece, Robert J.

    1997-01-01

    We present a general “message-passing” algorithm for distributing information in a graph. This algorithm may help us to understand the approximate correctness of both the Gallager-Tanner-Wiberg algorithm, and the turbo-decoding algorithm.

  20. Evaluation of Static JavaScript Call Graph Algorithms

    NARCIS (Netherlands)

    J.-J. Dijkstra (Jorryt-Jan)

    2014-01-01

    htmlabstractThis thesis consists of a replication study in which two algorithms to compute JavaScript call graphs have been implemented and evaluated. Existing IDE support for JavaScript is hampered due to the dynamic nature of the language. Previous studies partially solve call graph computation

  1. Parallel Algorithms for Switching Edges in Heterogeneous Graphs.

    Science.gov (United States)

    Bhuiyan, Hasanuzzaman; Khan, Maleq; Chen, Jiangzhuo; Marathe, Madhav

    2017-06-01

    An edge switch is an operation on a graph (or network) where two edges are selected randomly and one of their end vertices are swapped with each other. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks, and in studying various dynamic phenomena over a network. The recent growth of real-world networks motivates the need for efficient parallel algorithms. The dependencies among successive edge switch operations and the requirement to keep the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors leading to difficulties in achieving a good speedup by parallelization. In this paper, we present distributed memory parallel algorithms for switching edges in massive networks. These algorithms provide good speedup and scale well to a large number of processors. A harmonic mean speedup of 73.25 is achieved on eight different networks with 1024 processors. One of the steps in our edge switch algorithms requires the computation of multinomial random variables in parallel. This paper presents the first non-trivial parallel algorithm for the problem, achieving a speedup of 925 using 1024 processors.

  2. A hierarchical approach to reducing communication in parallel graph algorithms

    KAUST Repository

    Harshvardhan,

    2015-01-01

    Large-scale graph computing has become critical due to the ever-increasing size of data. However, distributed graph computations are limited in their scalability and performance due to the heavy communication inherent in such computations. This is exacerbated in scale-free networks, such as social and web graphs, which contain hub vertices that have large degrees and therefore send a large number of messages over the network. Furthermore, many graph algorithms and computations send the same data to each of the neighbors of a vertex. Our proposed approach recognizes this, and reduces communication performed by the algorithm without change to user-code, through a hierarchical machine model imposed upon the input graph. The hierarchical model takes advantage of locale information of the neighboring vertices to reduce communication, both in message volume and total number of bytes sent. It is also able to better exploit the machine hierarchy to further reduce the communication costs, by aggregating traffic between different levels of the machine hierarchy. Results of an implementation in the STAPL GL shows improved scalability and performance over the traditional level-synchronous approach, with 2.5 × - 8× improvement for a variety of graph algorithms at 12, 000+ cores.

  3. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector

    2017-07-08

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure\\'s range of applications and demonstrating the weaknesses of computable measures of complexity.

  4. Low-algorithmic-complexity entropy-deceiving graphs

    KAUST Repository

    Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

    2017-01-01

    In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

  5. The graph-theoretic minimum energy path problem for ionic conduction

    Directory of Open Access Journals (Sweden)

    Ippei Kishida

    2015-10-01

    Full Text Available A new computational method was developed to analyze the ionic conduction mechanism in crystals through graph theory. The graph was organized into nodes, which represent the crystal structures modeled by ionic site occupation, and edges, which represent structure transitions via ionic jumps. We proposed a minimum energy path problem, which is similar to the shortest path problem. An effective algorithm to solve the problem was established. Since our method does not use randomized algorithm and time parameters, the computational cost to analyze conduction paths and a migration energy is very low. The power of the method was verified by applying it to α-AgI and the ionic conduction mechanism in α-AgI was revealed. The analysis using single point calculations found the minimum energy path for long-distance ionic conduction, which consists of 12 steps of ionic jumps in a unit cell. From the results, the detailed theoretical migration energy was calculated as 0.11 eV by geometry optimization and nudged elastic band method. Our method can refine candidates for possible jumps in crystals and it can be adapted to other computational methods, such as the nudged elastic band method. We expect that our method will be a powerful tool for analyzing ionic conduction mechanisms, even for large complex crystals.

  6. Model of twelve properties of a set of organic solvents with graph-theoretical and/or experimental parameters.

    Science.gov (United States)

    Pogliani, Lionello

    2010-01-30

    Twelve properties of a highly heterogeneous class of organic solvents have been modeled with a graph-theoretical molecular connectivity modified (MC) method, which allows to encode the core electrons and the hydrogen atoms. The graph-theoretical method uses the concepts of simple, general, and complete graphs, where these last types of graphs are used to encode the core electrons. The hydrogen atoms have been encoded by the aid of a graph-theoretical perturbation parameter, which contributes to the definition of the valence delta, delta(v), a key parameter in molecular connectivity studies. The model of the twelve properties done with a stepwise search algorithm is always satisfactory, and it allows to check the influence of the hydrogen content of the solvent molecules on the choice of the type of descriptor. A similar argument holds for the influence of the halogen atoms on the type of core electron representation. In some cases the molar mass, and in a minor way, special "ad hoc" parameters have been used to improve the model. A very good model of the surface tension could be obtained by the aid of five experimental parameters. A mixed model method based on experimental parameters plus molecular connectivity indices achieved, instead, to consistently improve the model quality of five properties. To underline is the importance of the boiling point temperatures as descriptors in these last two model methodologies. Copyright 2009 Wiley Periodicals, Inc.

  7. Graph theoretical model of a sensorimotor connectome in zebrafish.

    Science.gov (United States)

    Stobb, Michael; Peterson, Joshua M; Mazzag, Borbala; Gahtan, Ethan

    2012-01-01

    Mapping the detailed connectivity patterns (connectomes) of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron) varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

  8. RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology.

    Directory of Open Access Journals (Sweden)

    Namhee Kim

    Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs

  9. A simple greedy algorithm for dynamic graph orientation

    DEFF Research Database (Denmark)

    Berglin, Edvin; Brodal, Gerth Stølting

    2017-01-01

    Graph orientations with low out-degree are one of several ways to efficiently store sparse graphs. If the graphs allow for insertion and deletion of edges, one may have to flip the orientation of some edges to prevent blowing up the maximum out-degree. We use arboricity as our sparsity measure....... With an immensely simple greedy algorithm, we get parametrized trade-off bounds between out-degree and worst case number of flips, which previously only existed for amortized number of flips. We match the previous best worst-case algorithm (in O(log n) flips) for general arboricity and beat it for either constant...... or super-logarithmic arboricity. We also match a previous best amortized result for at least logarithmic arboricity, and give the first results with worst-case O(1) and O(sqrt(log n)) flips nearly matching degree bounds to their respective amortized solutions....

  10. Graph theoretical model of a sensorimotor connectome in zebrafish.

    Directory of Open Access Journals (Sweden)

    Michael Stobb

    Full Text Available Mapping the detailed connectivity patterns (connectomes of neural circuits is a central goal of neuroscience. The best quantitative approach to analyzing connectome data is still unclear but graph theory has been used with success. We present a graph theoretical model of the posterior lateral line sensorimotor pathway in zebrafish. The model includes 2,616 neurons and 167,114 synaptic connections. Model neurons represent known cell types in zebrafish larvae, and connections were set stochastically following rules based on biological literature. Thus, our model is a uniquely detailed computational representation of a vertebrate connectome. The connectome has low overall connection density, with 2.45% of all possible connections, a value within the physiological range. We used graph theoretical tools to compare the zebrafish connectome graph to small-world, random and structured random graphs of the same size. For each type of graph, 100 randomly generated instantiations were considered. Degree distribution (the number of connections per neuron varied more in the zebrafish graph than in same size graphs with less biological detail. There was high local clustering and a short average path length between nodes, implying a small-world structure similar to other neural connectomes and complex networks. The graph was found not to be scale-free, in agreement with some other neural connectomes. An experimental lesion was performed that targeted three model brain neurons, including the Mauthner neuron, known to control fast escape turns. The lesion decreased the number of short paths between sensory and motor neurons analogous to the behavioral effects of the same lesion in zebrafish. This model is expandable and can be used to organize and interpret a growing database of information on the zebrafish connectome.

  11. Parallel algorithms for finding cliques in a graph

    International Nuclear Information System (INIS)

    Szabo, S

    2011-01-01

    A clique is a subgraph in a graph that is complete in the sense that each two of its nodes are connected by an edge. Finding cliques in a given graph is an important procedure in discrete mathematical modeling. The paper will show how concepts such as splitting partitions, quasi coloring, node and edge dominance are related to clique search problems. In particular we will discuss the connection with parallel clique search algorithms. These concepts also suggest practical guide lines to inspect a given graph before starting a large scale search.

  12. Connectivity algorithm with depth first search (DFS) on simple graphs

    Science.gov (United States)

    Riansanti, O.; Ihsan, M.; Suhaimi, D.

    2018-01-01

    This paper discusses an algorithm to detect connectivity of a simple graph using Depth First Search (DFS). The DFS implementation in this paper differs than other research, that is, on counting the number of visited vertices. The algorithm obtains s from the number of vertices and visits source vertex, following by its adjacent vertices until the last vertex adjacent to the previous source vertex. Any simple graph is connected if s equals 0 and disconnected if s is greater than 0. The complexity of the algorithm is O(n2).

  13. EAGLE: 'EAGLE'Is an' Algorithmic Graph Library for Exploration

    Energy Technology Data Exchange (ETDEWEB)

    2015-01-16

    The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. Today there is no tools to conduct "graph mining" on RDF standard data sets. We address that need through implementation of popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, degree distribution, diversity degree, PageRank, etc.). We implement these algorithms as SPARQL queries, wrapped within Python scripts and call our software tool as EAGLE. In RDF style, EAGLE stands for "EAGLE 'Is an' algorithmic graph library for exploration. EAGLE is like 'MATLAB' for 'Linked Data.'

  14. On the design of a hierarchical SS7 network: A graph theoretical approach

    Science.gov (United States)

    Krauss, Lutz; Rufa, Gerhard

    1994-04-01

    This contribution is concerned with the design of Signaling System No. 7 networks based on graph theoretical methods. A hierarchical network topology is derived by combining the advantage of the hierarchical network structure with the realization of node disjoint routes between nodes of the network. By using specific features of this topology, we develop an algorithm to construct circle-free routing data and to assure bidirectionality also in case of failure situations. The methods described are based on the requirements that the network topology, as well as the routing data, may be easily changed.

  15. Algorithm for shortest path search in Geographic Information Systems by using reduced graphs.

    Science.gov (United States)

    Rodríguez-Puente, Rafael; Lazo-Cortés, Manuel S

    2013-01-01

    The use of Geographic Information Systems has increased considerably since the eighties and nineties. As one of their most demanding applications we can mention shortest paths search. Several studies about shortest path search show the feasibility of using graphs for this purpose. Dijkstra's algorithm is one of the classic shortest path search algorithms. This algorithm is not well suited for shortest path search in large graphs. This is the reason why various modifications to Dijkstra's algorithm have been proposed by several authors using heuristics to reduce the run time of shortest path search. One of the most used heuristic algorithms is the A* algorithm, the main goal is to reduce the run time by reducing the search space. This article proposes a modification of Dijkstra's shortest path search algorithm in reduced graphs. It shows that the cost of the path found in this work, is equal to the cost of the path found using Dijkstra's algorithm in the original graph. The results of finding the shortest path, applying the proposed algorithm, Dijkstra's algorithm and A* algorithm, are compared. This comparison shows that, by applying the approach proposed, it is possible to obtain the optimal path in a similar or even in less time than when using heuristic algorithms.

  16. A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains

    Science.gov (United States)

    Gan, Tingyue; Cameron, Maria

    2017-06-01

    Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical timescales at which the qualitative behavior of a given Markov chain changes, and give an effective description of the dynamics on each of them. This approach is valid for both time-reversible and time-irreversible Markov processes, with or without symmetry. Central to this approach are two graph algorithms, Algorithm 1 and Algorithm 2, for obtaining the sequences of the critical timescales and the hierarchies of Typical Transition Graphs or T-graphs indicating the most likely transitions in the system without and with symmetry, respectively. The sequence of critical timescales includes the subsequence of the reciprocals of the real parts of eigenvalues. Under a certain assumption, we prove sharp asymptotic estimates for eigenvalues (including pre-factors) and show how one can extract them from the output of Algorithm 1. We discuss the relationship between Algorithms 1 and 2 and explain how one needs to interpret the output of Algorithm 1 if it is applied in the case with symmetry instead of Algorithm 2. Finally, we analyze an example motivated by R. D. Astumian's model of the dynamics of kinesin, a molecular motor, by means of Algorithm 2.

  17. Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs

    Directory of Open Access Journals (Sweden)

    Vaughn Matthew

    2010-11-01

    Full Text Available Abstract Background Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories - based on the data structures which they employ. The first class uses an overlap/string graph and the second type uses a de Bruijn graph. However with the recent advances in short read sequencing technology, de Bruijn graph based algorithms seem to play a vital role in practice. Efficient algorithms for building these massive de Bruijn graphs are very essential in large sequencing projects based on short reads. In an earlier work, an O(n/p time parallel algorithm has been given for this problem. Here n is the size of the input and p is the number of processors. This algorithm enumerates all possible bi-directed edges which can overlap with a node and ends up generating Θ(nΣ messages (Σ being the size of the alphabet. Results In this paper we present a Θ(n/p time parallel algorithm with a communication complexity that is equal to that of parallel sorting and is not sensitive to Σ. The generality of our algorithm makes it very easy to extend it even to the out-of-core model and in this case it has an optimal I/O complexity of Θ(nlog(n/BBlog(M/B (M being the main memory size and B being the size of the disk block. We demonstrate the scalability of our parallel algorithm on a SGI/Altix computer. A comparison of our algorithm with the previous approaches reveals that our algorithm is faster - both asymptotically and practically. We demonstrate the scalability of our sequential out-of-core algorithm by comparing it with the algorithm used by VELVET to build the bi-directed de Bruijn graph. Our experiments reveal that our algorithm can build the graph with a constant amount of memory, which clearly outperforms VELVET. We also provide efficient algorithms for the bi-directed chain compaction problem. Conclusions The bi

  18. Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.

    Science.gov (United States)

    Kundeti, Vamsi K; Rajasekaran, Sanguthevar; Dinh, Hieu; Vaughn, Matthew; Thapar, Vishal

    2010-11-15

    Assembling genomic sequences from a set of overlapping reads is one of the most fundamental problems in computational biology. Algorithms addressing the assembly problem fall into two broad categories - based on the data structures which they employ. The first class uses an overlap/string graph and the second type uses a de Bruijn graph. However with the recent advances in short read sequencing technology, de Bruijn graph based algorithms seem to play a vital role in practice. Efficient algorithms for building these massive de Bruijn graphs are very essential in large sequencing projects based on short reads. In an earlier work, an O(n/p) time parallel algorithm has been given for this problem. Here n is the size of the input and p is the number of processors. This algorithm enumerates all possible bi-directed edges which can overlap with a node and ends up generating Θ(nΣ) messages (Σ being the size of the alphabet). In this paper we present a Θ(n/p) time parallel algorithm with a communication complexity that is equal to that of parallel sorting and is not sensitive to Σ. The generality of our algorithm makes it very easy to extend it even to the out-of-core model and in this case it has an optimal I/O complexity of Θ(nlog(n/B)Blog(M/B)) (M being the main memory size and B being the size of the disk block). We demonstrate the scalability of our parallel algorithm on a SGI/Altix computer. A comparison of our algorithm with the previous approaches reveals that our algorithm is faster--both asymptotically and practically. We demonstrate the scalability of our sequential out-of-core algorithm by comparing it with the algorithm used by VELVET to build the bi-directed de Bruijn graph. Our experiments reveal that our algorithm can build the graph with a constant amount of memory, which clearly outperforms VELVET. We also provide efficient algorithms for the bi-directed chain compaction problem. The bi-directed de Bruijn graph is a fundamental data structure for

  19. Development of antibiotic regimens using graph based evolutionary algorithms.

    Science.gov (United States)

    Corns, Steven M; Ashlock, Daniel A; Bryden, Kenneth M

    2013-12-01

    This paper examines the use of evolutionary algorithms in the development of antibiotic regimens given to production animals. A model is constructed that combines the lifespan of the animal and the bacteria living in the animal's gastro-intestinal tract from the early finishing stage until the animal reaches market weight. This model is used as the fitness evaluation for a set of graph based evolutionary algorithms to assess the impact of diversity control on the evolving antibiotic regimens. The graph based evolutionary algorithms have two objectives: to find an antibiotic treatment regimen that maintains the weight gain and health benefits of antibiotic use and to reduce the risk of spreading antibiotic resistant bacteria. This study examines different regimens of tylosin phosphate use on bacteria populations divided into Gram positive and Gram negative types, with a focus on Campylobacter spp. Treatment regimens were found that provided decreased antibiotic resistance relative to conventional methods while providing nearly the same benefits as conventional antibiotic regimes. By using a graph to control the information flow in the evolutionary algorithm, a variety of solutions along the Pareto front can be found automatically for this and other multi-objective problems. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  20. A hierarchical approach to reducing communication in parallel graph algorithms

    KAUST Repository

    Harshvardhan,; Amato, Nancy M.; Rauchwerger, Lawrence

    2015-01-01

    . This is exacerbated in scale-free networks, such as social and web graphs, which contain hub vertices that have large degrees and therefore send a large number of messages over the network. Furthermore, many graph algorithms and computations send the same data to each

  1. Parallel External Memory Graph Algorithms

    DEFF Research Database (Denmark)

    Arge, Lars Allan; Goodrich, Michael T.; Sitchinava, Nodari

    2010-01-01

    In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one o f the private-cache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to efficient solutions to problems on trees, such as computing lowest...... an optimal speedup of ¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....

  2. An algorithmic decomposition of claw-free graphs leading to an O(n^3) algorithm for the weighted stable set problem

    OpenAIRE

    Faenza, Y.; Oriolo, G.; Stauffer, G.

    2011-01-01

    We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(n^3)-time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition theorem for claw-free graphs, which is also intioduced in the present paper. Despite being weaker than the well-known structure result for claw-free graphs given by Chudnovsky and Seymour, our decomposition theorem is, on the other hand, algorithmic, i.e. it is ...

  3. Exponential-Time Algorithms and Complexity of NP-Hard Graph Problems

    DEFF Research Database (Denmark)

    Taslaman, Nina Sofia

    of algorithms, as well as investigations into how far such improvements can get under reasonable assumptions.      The first part is concerned with detection of cycles in graphs, especially parameterized generalizations of Hamiltonian cycles. A remarkably simple Monte Carlo algorithm is presented......NP-hard problems are deemed highly unlikely to be solvable in polynomial time. Still, one can often find algorithms that are substantially faster than brute force solutions. This thesis concerns such algorithms for problems from graph theory; techniques for constructing and improving this type......, and with high probability any found solution is shortest possible. Moreover, the algorithm can be used to find a cycle of given parity through the specified elements.      The second part concerns the hardness of problems encoded as evaluations of the Tutte polynomial at some fixed point in the rational plane...

  4. Multi-scale graph-cut algorithm for efficient water-fat separation.

    Science.gov (United States)

    Berglund, Johan; Skorpil, Mikael

    2017-09-01

    To improve the accuracy and robustness to noise in water-fat separation by unifying the multiscale and graph cut based approaches to B 0 -correction. A previously proposed water-fat separation algorithm that corrects for B 0 field inhomogeneity in 3D by a single quadratic pseudo-Boolean optimization (QPBO) graph cut was incorporated into a multi-scale framework, where field map solutions are propagated from coarse to fine scales for voxels that are not resolved by the graph cut. The accuracy of the single-scale and multi-scale QPBO algorithms was evaluated against benchmark reference datasets. The robustness to noise was evaluated by adding noise to the input data prior to water-fat separation. Both algorithms achieved the highest accuracy when compared with seven previously published methods, while computation times were acceptable for implementation in clinical routine. The multi-scale algorithm was more robust to noise than the single-scale algorithm, while causing only a small increase (+10%) of the reconstruction time. The proposed 3D multi-scale QPBO algorithm offers accurate water-fat separation, robustness to noise, and fast reconstruction. The software implementation is freely available to the research community. Magn Reson Med 78:941-949, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

  5. Personalized PageRank Clustering: A graph clustering algorithm based on random walks

    Science.gov (United States)

    A. Tabrizi, Shayan; Shakery, Azadeh; Asadpour, Masoud; Abbasi, Maziar; Tavallaie, Mohammad Ali

    2013-11-01

    Graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications. In addition, exponential growth of real-world graphs such as social networks, biological networks and electrical circuits demands clustering algorithms with nearly-linear time and space complexity. In this paper we propose Personalized PageRank Clustering (PPC) that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph. We combine random walks and modularity to precisely and efficiently reveal the clusters of a graph. PPC is a top-down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly-linear approaches that are mainly bottom-up. It also gives a hierarchy of clusters that is useful in many applications. PPC has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets. Furthermore, its top-down approach makes it a flexible solution for clustering problems with different requirements.

  6. A novel line segment detection algorithm based on graph search

    Science.gov (United States)

    Zhao, Hong-dan; Liu, Guo-ying; Song, Xu

    2018-02-01

    To overcome the problem of extracting line segment from an image, a method of line segment detection was proposed based on the graph search algorithm. After obtaining the edge detection result of the image, the candidate straight line segments are obtained in four directions. For the candidate straight line segments, their adjacency relationships are depicted by a graph model, based on which the depth-first search algorithm is employed to determine how many adjacent line segments need to be merged. Finally we use the least squares method to fit the detected straight lines. The comparative experimental results verify that the proposed algorithm has achieved better results than the line segment detector (LSD).

  7. Analysis and enumeration algorithms for biological graphs

    CERN Document Server

    Marino, Andrea

    2015-01-01

    In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions...

  8. A HYBRID ALGORITHM FOR THE ROBUST GRAPH COLORING PROBLEM

    Directory of Open Access Journals (Sweden)

    Román Anselmo Mora Gutiérrez

    2016-08-01

    Full Text Available A hybridalgorithm which combines mathematical programming techniques (Kruskal’s algorithm and the strategy of maintaining arc consistency to solve constraint satisfaction problem “CSP” and heuristic methods (musical composition method and DSATUR to resolve the robust graph coloring problem (RGCP is proposed in this paper. Experimental result shows that this algorithm is better than the other algorithms presented on the literature.

  9. Algorithms and Models for the Web Graph

    NARCIS (Netherlands)

    Gleich, David F.; Komjathy, Julia; Litvak, Nelli

    2015-01-01

    This volume contains the papers presented at WAW2015, the 12th Workshop on Algorithms and Models for the Web-Graph held during December 10–11, 2015, in Eindhoven. There were 24 submissions. Each submission was reviewed by at least one, and on average two, Program Committee members. The committee

  10. Memoryless cooperative graph search based on the simulated annealing algorithm

    International Nuclear Information System (INIS)

    Hou Jian; Yan Gang-Feng; Fan Zhen

    2011-01-01

    We have studied the problem of reaching a globally optimal segment for a graph-like environment with a single or a group of autonomous mobile agents. Firstly, two efficient simulated-annealing-like algorithms are given for a single agent to solve the problem in a partially known environment and an unknown environment, respectively. It shows that under both proposed control strategies, the agent will eventually converge to a globally optimal segment with probability 1. Secondly, we use multi-agent searching to simultaneously reduce the computation complexity and accelerate convergence based on the algorithms we have given for a single agent. By exploiting graph partition, a gossip-consensus method based scheme is presented to update the key parameter—radius of the graph, ensuring that the agents spend much less time finding a globally optimal segment. (interdisciplinary physics and related areas of science and technology)

  11. AN EFFECTIVE RECOMMENDATIONS BY DIFFUSION ALGORITHM FOR WEB GRAPH MINING

    Directory of Open Access Journals (Sweden)

    S. Vasukipriya

    2013-04-01

    Full Text Available The information on the World Wide Web grows in an explosive rate. Societies are relying more on the Web for their miscellaneous needs of information. Recommendation systems are active information filtering systems that attempt to present the information items like movies, music, images, books recommendations, tags recommendations, query suggestions, etc., to the users. Various kinds of data bases are used for the recommendations; fundamentally these data bases can be molded in the form of many types of graphs. Aiming at provided that a general framework on effective DR (Recommendations by Diffusion algorithm for web graphs mining. First introduce a novel graph diffusion model based on heat diffusion. This method can be applied to both undirected graphs and directed graphs. Then it shows how to convert different Web data sources into correct graphs in our models.

  12. Fitchi: haplotype genealogy graphs based on the Fitch algorithm.

    Science.gov (United States)

    Matschiner, Michael

    2016-04-15

    : In population genetics and phylogeography, haplotype genealogy graphs are important tools for the visualization of population structure based on sequence data. In this type of graph, node sizes are often drawn in proportion to haplotype frequencies and edge lengths represent the minimum number of mutations separating adjacent nodes. I here present Fitchi, a new program that produces publication-ready haplotype genealogy graphs based on the Fitch algorithm. http://www.evoinformatics.eu/fitchi.htm : michaelmatschiner@mac.com Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

  13. External Memory Algorithms for Diameter and All-Pair Shortest-Paths on Sparse Graphs

    DEFF Research Database (Denmark)

    Arge, Lars; Meyer, Ulrich; Toma, Laura

    2004-01-01

    We present several new external-memory algorithms for finding all-pairs shortest paths in a V -node, Eedge undirected graph. For all-pairs shortest paths and diameter in unweighted undirected graphs we present cache-oblivious algorithms with O(V · E B logM B E B) I/Os, where B is the block-size a...

  14. Graph theory

    CERN Document Server

    Gould, Ronald

    2012-01-01

    This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S

  15. Semantic Drift in Espresso-style Bootstrapping: Graph-theoretic Analysis and Evaluation in Word Sense Disambiguation

    Science.gov (United States)

    Komachi, Mamoru; Kudo, Taku; Shimbo, Masashi; Matsumoto, Yuji

    Bootstrapping has a tendency, called semantic drift, to select instances unrelated to the seed instances as the iteration proceeds. We demonstrate the semantic drift of Espresso-style bootstrapping has the same root as the topic drift of Kleinberg's HITS, using a simplified graph-based reformulation of bootstrapping. We confirm that two graph-based algorithms, the von Neumann kernels and the regularized Laplacian, can reduce the effect of semantic drift in the task of word sense disambiguation (WSD) on Senseval-3 English Lexical Sample Task. Proposed algorithms achieve superior performance to Espresso and previous graph-based WSD methods, even though the proposed algorithms have less parameters and are easy to calibrate.

  16. Pathfinding in graph-theoretic sabotage models. I. Simultaneous attack by several teams

    International Nuclear Information System (INIS)

    Hulme, B.L.

    1976-07-01

    Graph models are developed for fixed-site safeguards systems. The problem of finding optimal routes for several sabotage teams is cast as a problem of finding shortest paths in a graph. The motivation, rationale, and interpretation of the mathematical models are discussed in detail, and an algorithm for efficiently solving the associated path problem is described

  17. Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs

    KAUST Repository

    Jamour, Fuad Tarek; Skiadopoulos, Spiros; Kalnis, Panos

    2017-01-01

    : they either require excessive memory (i.e., quadratic to the size of the input graph) or perform unnecessary computations rendering them prohibitively slow. We propose iCentral; a novel incremental algorithm for computing betweenness centrality in evolving

  18. Graph Transformation and Designing Parallel Sparse Matrix Algorithms beyond Data Dependence Analysis

    Directory of Open Access Journals (Sweden)

    H.X. Lin

    2004-01-01

    Full Text Available Algorithms are often parallelized based on data dependence analysis manually or by means of parallel compilers. Some vector/matrix computations such as the matrix-vector products with simple data dependence structures (data parallelism can be easily parallelized. For problems with more complicated data dependence structures, parallelization is less straightforward. The data dependence graph is a powerful means for designing and analyzing parallel algorithms. However, for sparse matrix computations, parallelization based on solely exploiting the existing parallelism in an algorithm does not always give satisfactory results. For example, the conventional Gaussian elimination algorithm for the solution of a tri-diagonal system is inherently sequential, so algorithms specially for parallel computation has to be designed. After briefly reviewing different parallelization approaches, a powerful graph formalism for designing parallel algorithms is introduced. This formalism will be discussed using a tri-diagonal system as an example. Its application to general matrix computations is also discussed. Its power in designing parallel algorithms beyond the ability of data dependence analysis is shown by means of a new algorithm called ACER (Alternating Cyclic Elimination and Reduction algorithm.

  19. A comparison of graph- and kernel-based -omics data integration algorithms for classifying complex traits.

    Science.gov (United States)

    Yan, Kang K; Zhao, Hongyu; Pang, Herbert

    2017-12-06

    High-throughput sequencing data are widely collected and analyzed in the study of complex diseases in quest of improving human health. Well-studied algorithms mostly deal with single data source, and cannot fully utilize the potential of these multi-omics data sources. In order to provide a holistic understanding of human health and diseases, it is necessary to integrate multiple data sources. Several algorithms have been proposed so far, however, a comprehensive comparison of data integration algorithms for classification of binary traits is currently lacking. In this paper, we focus on two common classes of integration algorithms, graph-based that depict relationships with subjects denoted by nodes and relationships denoted by edges, and kernel-based that can generate a classifier in feature space. Our paper provides a comprehensive comparison of their performance in terms of various measurements of classification accuracy and computation time. Seven different integration algorithms, including graph-based semi-supervised learning, graph sharpening integration, composite association network, Bayesian network, semi-definite programming-support vector machine (SDP-SVM), relevance vector machine (RVM) and Ada-boost relevance vector machine are compared and evaluated with hypertension and two cancer data sets in our study. In general, kernel-based algorithms create more complex models and require longer computation time, but they tend to perform better than graph-based algorithms. The performance of graph-based algorithms has the advantage of being faster computationally. The empirical results demonstrate that composite association network, relevance vector machine, and Ada-boost RVM are the better performers. We provide recommendations on how to choose an appropriate algorithm for integrating data from multiple sources.

  20. Time- and Cost-Optimal Parallel Algorithms for the Dominance and Visibility Graphs

    Directory of Open Access Journals (Sweden)

    D. Bhagavathi

    1996-01-01

    Full Text Available The compaction step of integrated circuit design motivates associating several kinds of graphs with a collection of non-overlapping rectangles in the plane. These graphs are intended to capture various visibility relations amongst the rectangles in the collection. The contribution of this paper is to propose time- and cost-optimal algorithms to construct two such graphs, namely, the dominance graph (DG, for short and the visibility graph (VG, for short. Specifically, we show that with a collection of n non-overlapping rectangles as input, both these structures can be constructed in θ(log n time using n processors in the CREW model.

  1. A graph rewriting programming language for graph drawing

    OpenAIRE

    Rodgers, Peter

    1998-01-01

    This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...

  2. Graph theoretical calculation of systems reliability with semi-Markov processes

    International Nuclear Information System (INIS)

    Widmer, U.

    1984-06-01

    The determination of the state probabilities and related quantities of a system characterized by an SMP (or a homogeneous MP) can be performed by means of graph-theoretical methods. The calculation procedures for semi-Markov processes based on signal flow graphs are reviewed. Some methods from electrotechnics are adapted in order to obtain a representation of the state probabilities by means of trees. From this some formulas are derived for the asymptotic state probabilities and for the mean life-time in reliability considerations. (Auth.)

  3. Automated intraretinal layer segmentation of optical coherence tomography images using graph-theoretical methods

    Science.gov (United States)

    Roy, Priyanka; Gholami, Peyman; Kuppuswamy Parthasarathy, Mohana; Zelek, John; Lakshminarayanan, Vasudevan

    2018-02-01

    Segmentation of spectral-domain Optical Coherence Tomography (SD-OCT) images facilitates visualization and quantification of sub-retinal layers for diagnosis of retinal pathologies. However, manual segmentation is subjective, expertise dependent, and time-consuming, which limits applicability of SD-OCT. Efforts are therefore being made to implement active-contours, artificial intelligence, and graph-search to automatically segment retinal layers with accuracy comparable to that of manual segmentation, to ease clinical decision-making. Although, low optical contrast, heavy speckle noise, and pathologies pose challenges to automated segmentation. Graph-based image segmentation approach stands out from the rest because of its ability to minimize the cost function while maximising the flow. This study has developed and implemented a shortest-path based graph-search algorithm for automated intraretinal layer segmentation of SD-OCT images. The algorithm estimates the minimal-weight path between two graph-nodes based on their gradients. Boundary position indices (BPI) are computed from the transition between pixel intensities. The mean difference between BPIs of two consecutive layers quantify individual layer thicknesses, which shows statistically insignificant differences when compared to a previous study [for overall retina: p = 0.17, for individual layers: p > 0.05 (except one layer: p = 0.04)]. These results substantiate the accurate delineation of seven intraretinal boundaries in SD-OCT images by this algorithm, with a mean computation time of 0.93 seconds (64-bit Windows10, core i5, 8GB RAM). Besides being self-reliant for denoising, the algorithm is further computationally optimized to restrict segmentation within the user defined region-of-interest. The efficiency and reliability of this algorithm, even in noisy image conditions, makes it clinically applicable.

  4. An effective trust-based recommendation method using a novel graph clustering algorithm

    Science.gov (United States)

    Moradi, Parham; Ahmadian, Sajad; Akhlaghian, Fardin

    2015-10-01

    Recommender systems are programs that aim to provide personalized recommendations to users for specific items (e.g. music, books) in online sharing communities or on e-commerce sites. Collaborative filtering methods are important and widely accepted types of recommender systems that generate recommendations based on the ratings of like-minded users. On the other hand, these systems confront several inherent issues such as data sparsity and cold start problems, caused by fewer ratings against the unknowns that need to be predicted. Incorporating trust information into the collaborative filtering systems is an attractive approach to resolve these problems. In this paper, we present a model-based collaborative filtering method by applying a novel graph clustering algorithm and also considering trust statements. In the proposed method first of all, the problem space is represented as a graph and then a sparsest subgraph finding algorithm is applied on the graph to find the initial cluster centers. Then, the proposed graph clustering algorithm is performed to obtain the appropriate users/items clusters. Finally, the identified clusters are used as a set of neighbors to recommend unseen items to the current active user. Experimental results based on three real-world datasets demonstrate that the proposed method outperforms several state-of-the-art recommender system methods.

  5. A Faster Algorithm for Computing Motorcycle Graphs

    KAUST Repository

    Vigneron, Antoine E.; Yan, Lie

    2014-01-01

    We present a new algorithm for computing motorcycle graphs that runs in (Formula presented.) time for any (Formula presented.), improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with (Formula presented.) holes in (Formula presented.) expected time. If all input coordinates are (Formula presented.)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with (Formula presented.) holes in (Formula presented.) expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in (Formula presented.) expected time if all input coordinates are (Formula presented.)-bit rationals, while all previously known algorithms have worst-case running time (Formula presented.). © 2014 Springer Science+Business Media New York.

  6. A Faster Algorithm for Computing Motorcycle Graphs

    KAUST Repository

    Vigneron, Antoine E.

    2014-08-29

    We present a new algorithm for computing motorcycle graphs that runs in (Formula presented.) time for any (Formula presented.), improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with (Formula presented.) holes in (Formula presented.) expected time. If all input coordinates are (Formula presented.)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with (Formula presented.) holes in (Formula presented.) expected time. In particular, it means that we can compute the straight skeleton of a simple polygon in (Formula presented.) expected time if all input coordinates are (Formula presented.)-bit rationals, while all previously known algorithms have worst-case running time (Formula presented.). © 2014 Springer Science+Business Media New York.

  7. Constructing a graph of connections in clustering algorithm of complex objects

    Directory of Open Access Journals (Sweden)

    Татьяна Шатовская

    2015-05-01

    Full Text Available The article describes the results of modifying the algorithm Chameleon. Hierarchical multi-level algorithm consists of several phases: the construction of the count, coarsening, the separation and recovery. Each phase can be used various approaches and algorithms. The main aim of the work is to study the quality of the clustering of different sets of data using a set of algorithms combinations at different stages of the algorithm and improve the stage of construction by the optimization algorithm of k choice in the graph construction of k of nearest neighbors

  8. Graph-drawing algorithms geometries versus molecular mechanics in fullereness

    Science.gov (United States)

    Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

    1996-09-01

    The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

  9. GraDit: graph-based data repair algorithm for multiple data edits rule violations

    Science.gov (United States)

    Ode Zuhayeni Madjida, Wa; Gusti Bagus Baskara Nugraha, I.

    2018-03-01

    Constraint-based data cleaning captures data violation to a set of rule called data quality rules. The rules consist of integrity constraint and data edits. Structurally, they are similar, where the rule contain left hand side and right hand side. Previous research proposed a data repair algorithm for integrity constraint violation. The algorithm uses undirected hypergraph as rule violation representation. Nevertheless, this algorithm can not be applied for data edits because of different rule characteristics. This study proposed GraDit, a repair algorithm for data edits rule. First, we use bipartite-directed hypergraph as model representation of overall defined rules. These representation is used for getting interaction between violation rules and clean rules. On the other hand, we proposed undirected graph as violation representation. Our experimental study showed that algorithm with undirected graph as violation representation model gave better data quality than algorithm with undirected hypergraph as representation model.

  10. Theoretical Bound of CRLB for Energy Efficient Technique of RSS-Based Factor Graph Geolocation

    Science.gov (United States)

    Kahar Aziz, Muhammad Reza; Heriansyah; Saputra, EfaMaydhona; Musa, Ardiansyah

    2018-03-01

    To support the increase of wireless geolocation development as the key of the technology in the future, this paper proposes theoretical bound derivation, i.e., Cramer Rao lower bound (CRLB) for energy efficient of received signal strength (RSS)-based factor graph wireless geolocation technique. The theoretical bound derivation is crucially important to evaluate whether the energy efficient technique of RSS-based factor graph wireless geolocation is effective as well as to open the opportunity to further innovation of the technique. The CRLB is derived in this paper by using the Fisher information matrix (FIM) of the main formula of the RSS-based factor graph geolocation technique, which is lied on the Jacobian matrix. The simulation result shows that the derived CRLB has the highest accuracy as a bound shown by its lowest root mean squared error (RMSE) curve compared to the RMSE curve of the RSS-based factor graph geolocation technique. Hence, the derived CRLB becomes the lower bound for the efficient technique of RSS-based factor graph wireless geolocation.

  11. Use of Graph-Theoretic Models in Technological Preparation of Assembly Plant

    Directory of Open Access Journals (Sweden)

    Peter Franzevich Yurchik

    2015-05-01

    Full Text Available The article examines the existing ways of describing the structural and technological properties of the product in the process of building and repair. It turned out that the main body of work on the preparation process of assembling production uses graph-theoretic model of the product. It is shown that, in general, the structural integrity of many-form connections and relations on the set of components that can not be adequately described by binary structures, such as graphs, networks or trees.

  12. Modification of MSDR algorithm and ITS implementation on graph clustering

    Science.gov (United States)

    Prastiwi, D.; Sugeng, K. A.; Siswantining, T.

    2017-07-01

    Maximum Standard Deviation Reduction (MSDR) is a graph clustering algorithm to minimize the distance variation within a cluster. In this paper we propose a modified MSDR by replacing one technical step in MSDR which uses polynomial regression, with a new and simpler step. This leads to our new algorithm called Modified MSDR (MMSDR). We implement the new algorithm to separate a domestic flight network of an Indonesian airline into two large clusters. Further analysis allows us to discover a weak link in the network, which should be improved by adding more flights.

  13. Chemical graph-theoretic cluster expansions

    International Nuclear Information System (INIS)

    Klein, D.J.

    1986-01-01

    A general computationally amenable chemico-graph-theoretic cluster expansion method is suggested as a paradigm for incorporation of chemical structure concepts in a systematic manner. The cluster expansion approach is presented in a formalism general enough to cover a variety of empirical, semiempirical, and even ab initio applications. Formally such approaches for the utilization of chemical structure-related concepts may be viewed as discrete analogues of Taylor series expansions. The efficacy of the chemical structure concepts then is simply bound up in the rate of convergence of the cluster expansions. In many empirical applications, e.g., boiling points, chromatographic separation coefficients, and biological activities, this rate of convergence has been observed to be quite rapid. More note will be made here of quantum chemical applications. Relations to questions concerning size extensivity of energies and size consistency of wave functions are addressed

  14. Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

    Science.gov (United States)

    Sur, Chiranjib; Shukla, Anupam

    2018-03-01

    Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

  15. Planar articulated mechanism design by graph theoretical enumeration

    DEFF Research Database (Denmark)

    Kawamoto, A; Bendsøe, Martin P.; Sigmund, Ole

    2004-01-01

    This paper deals with design of articulated mechanisms using a truss-based ground-structure representation. By applying a graph theoretical enumeration approach we can perform an exhaustive analysis of all possible topologies for a test example for which we seek a symmetric mechanism. This guaran....... This guarantees that one can identify the global optimum solution. The result underlines the importance of mechanism topology and gives insight into the issues specific to articulated mechanism designs compared to compliant mechanism designs....

  16. The STAPL Parallel Graph Library

    KAUST Repository

    Harshvardhan,

    2013-01-01

    This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.

  17. A Faster Algorithm to Recognize Even-Hole-Free Graphs

    OpenAIRE

    Chang, Hsien-Chih; Lu, Hsueh-I

    2013-01-01

    We study the problem of determining whether an $n$-node graph $G$ has an even hole, i.e., an induced simple cycle consisting of an even number of nodes. Conforti, Cornu\\'ejols, Kapoor, and Vu\\v{s}kovi\\'c gave the first polynomial-time algorithm for the problem, which runs in $O(n^{40})$ time. Later, Chudnovsky, Kawarabayashi, and Seymour reduced the running time to $O(n^{31})$. The best previously known algorithm for the problem, due to da Silva and Vu\\v{s}kovi\\'c, runs in $O(n^{19})$ time. I...

  18. A graph-Laplacian-based feature extraction algorithm for neural spike sorting.

    Science.gov (United States)

    Ghanbari, Yasser; Spence, Larry; Papamichalis, Panos

    2009-01-01

    Analysis of extracellular neural spike recordings is highly dependent upon the accuracy of neural waveform classification, commonly referred to as spike sorting. Feature extraction is an important stage of this process because it can limit the quality of clustering which is performed in the feature space. This paper proposes a new feature extraction method (which we call Graph Laplacian Features, GLF) based on minimizing the graph Laplacian and maximizing the weighted variance. The algorithm is compared with Principal Components Analysis (PCA, the most commonly-used feature extraction method) using simulated neural data. The results show that the proposed algorithm produces more compact and well-separated clusters compared to PCA. As an added benefit, tentative cluster centers are output which can be used to initialize a subsequent clustering stage.

  19. Computational Comparison of Several Greedy Algorithms for the Minimum Cost Perfect Matching Problem on Large Graphs

    DEFF Research Database (Denmark)

    Wøhlk, Sanne; Laporte, Gilbert

    2017-01-01

    The aim of this paper is to computationally compare several algorithms for the Minimum Cost Perfect Matching Problem on an undirected complete graph. Our work is motivated by the need to solve large instances of the Capacitated Arc Routing Problem (CARP) arising in the optimization of garbage...... collection in Denmark. Common heuristics for the CARP involve the optimal matching of the odd-degree nodes of a graph. The algorithms used in the comparison include the CPLEX solution of an exact formulation, the LEDA matching algorithm, a recent implementation of the Blossom algorithm, as well as six...

  20. Optimization of heat transfer utilizing graph based evolutionary algorithms

    International Nuclear Information System (INIS)

    Bryden, Kenneth M.; Ashlock, Daniel A.; McCorkle, Douglas S.; Urban, Gregory L.

    2003-01-01

    This paper examines the use of graph based evolutionary algorithms (GBEAs) for optimization of heat transfer in a complex system. The specific case examined in this paper is the optimization of heat transfer in a biomass cookstove utilizing three-dimensional computational fluid dynamics to generate the fitness function. In this stove hot combustion gases are used to heat a cooking surface. The goal is to provide an even spatial temperature distribution on the cooking surface by redirecting the flow of combustion gases with baffles. The variables in the optimization are the position and size of the baffles, which are described by integer values. GBEAs are a novel type of EA in which a topology or geography is imposed on an evolving population of solutions. The choice of graph controls the rate at which solutions can spread within the population, impacting the diversity of solutions and convergence rate of the EAs. In this study, the choice of graph in the GBEAs changes the number of mating events required for convergence by a factor of approximately 2.25 and the diversity of the population by a factor of 2. These results confirm that by tuning the graph and parameters in GBEAs, computational time can be significantly reduced

  1. Graphing trillions of triangles.

    Science.gov (United States)

    Burkhardt, Paul

    2017-07-01

    The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

  2. X-Graphs: Language and Algorithms for Heterogeneous Graph Streams

    Science.gov (United States)

    2017-09-01

    are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph

  3. Canonical Labelling of Site Graphs

    Directory of Open Access Journals (Sweden)

    Nicolas Oury

    2013-06-01

    Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.

  4. Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

    KAUST Repository

    Mahayni, Malek A.

    2011-07-01

    Finding optimal paths in directed graphs is a wide area of research that has received much of attention in theoretical computer science due to its importance in many applications (e.g., computer networks and road maps). Many algorithms have been developed to solve the optimal paths problem with different kinds of graphs. An algorithm that solves the problem of paths’ optimization in directed graphs relative to different cost functions is described in [1]. It follows an approach extended from the dynamic programming approach as it solves the problem sequentially and works on directed graphs with positive weights and no loop edges. The aim of this thesis is to implement and evaluate that algorithm to find the optimal paths in directed graphs relative to two different cost functions ( , ). A possible interpretation of a directed graph is a network of roads so the weights for the function represent the length of roads, whereas the weights for the function represent a constraint of the width or weight of a vehicle. The optimization aim for those two functions is to minimize the cost relative to the function and maximize the constraint value associated with the function. This thesis also includes finding and proving the relation between the two different cost functions ( , ). When given a value of one function, we can find the best possible value for the other function. This relation is proven theoretically and also implemented and experimented using Matlab®[2].

  5. Generating random networks and graphs

    CERN Document Server

    Coolen, Ton; Roberts, Ekaterina

    2017-01-01

    This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...

  6. Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

    International Nuclear Information System (INIS)

    Rosicka, M; Ramanathan, R; Gnaciński, P; Horodecki, M; Horodecki, K; Horodecki, P; Severini, S

    2016-01-01

    We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions. (paper)

  7. Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

    Science.gov (United States)

    Rosicka, M.; Ramanathan, R.; Gnaciński, P.; Horodecki, K.; Horodecki, M.; Horodecki, P.; Severini, S.

    2016-04-01

    We study the classical and quantum values of a class of one- and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR (XOR-d) games we study are a subclass of the well-known linear games. We introduce a ‘constraint graph’ associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lovász theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. XOR-d games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite XOR-d game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions.

  8. Tractable Algorithms for Proximity Search on Large Graphs

    Science.gov (United States)

    2010-07-01

    Education never ends, Watson. It is a series of lessons with the greatest for the last. — Sir Arthur Conan Doyle’s Sherlock Holmes . 2.1 Introduction A...Doyle’s Sherlock Holmes . 5.1 Introduction In this thesis, our main goal is to design fast algorithms for proximity search in large graphs. In chapter 3...Conan Doyle’s Sherlock Holmes . In this thesis our main focus is on investigating some useful random walk based prox- imity measures. We have started

  9. Information-optimal genome assembly via sparse read-overlap graphs.

    Science.gov (United States)

    Shomorony, Ilan; Kim, Samuel H; Courtade, Thomas A; Tse, David N C

    2016-09-01

    In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. Available at github.com/samhykim/nsg courtade@eecs.berkeley.edu or dntse@stanford.edu Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

  10. Coupling graph perturbation theory with scalable parallel algorithms for large-scale enumeration of maximal cliques in biological graphs

    International Nuclear Information System (INIS)

    Samatova, N F; Schmidt, M C; Hendrix, W; Breimyer, P; Thomas, K; Park, B-H

    2008-01-01

    Data-driven construction of predictive models for biological systems faces challenges from data intensity, uncertainty, and computational complexity. Data-driven model inference is often considered a combinatorial graph problem where an enumeration of all feasible models is sought. The data-intensive and the NP-hard nature of such problems, however, challenges existing methods to meet the required scale of data size and uncertainty, even on modern supercomputers. Maximal clique enumeration (MCE) in a graph derived from such biological data is often a rate-limiting step in detecting protein complexes in protein interaction data, finding clusters of co-expressed genes in microarray data, or identifying clusters of orthologous genes in protein sequence data. We report two key advances that address this challenge. We designed and implemented the first (to the best of our knowledge) parallel MCE algorithm that scales linearly on thousands of processors running MCE on real-world biological networks with thousands and hundreds of thousands of vertices. In addition, we proposed and developed the Graph Perturbation Theory (GPT) that establishes a foundation for efficiently solving the MCE problem in perturbed graphs, which model the uncertainty in the data. GPT formulates necessary and sufficient conditions for detecting the differences between the sets of maximal cliques in the original and perturbed graphs and reduces the enumeration time by more than 80% compared to complete recomputation

  11. Detecting Network Vulnerabilities Through Graph TheoreticalMethods

    Energy Technology Data Exchange (ETDEWEB)

    Cesarz, Patrick; Pomann, Gina-Maria; Torre, Luis de la; Villarosa, Greta; Flournoy, Tamara; Pinar, Ali; Meza Juan

    2007-09-30

    Identifying vulnerabilities in power networks is an important problem, as even a small number of vulnerable connections can cause billions of dollars in damage to a network. In this paper, we investigate a graph theoretical formulation for identifying vulnerabilities of a network. We first try to find the most critical components in a network by finding an optimal solution for each possible cutsize constraint for the relaxed version of the inhibiting bisection problem, which aims to find loosely coupled subgraphs with significant demand/supply mismatch. Then we investigate finding critical components by finding a flow assignment that minimizes the maximum among flow assignments on all edges. We also report experiments on IEEE 30, IEEE 118, and WSCC 179 benchmark power networks.

  12. Algorithms and Data Structures for Graphs

    DEFF Research Database (Denmark)

    Rotenberg, Eva

    are planar graphs, which are those that can be drawn on a piece of paper without any pair of edges crossing. For planar graphs where each edge can only be traversed in one direction, a fundamental question is whether there is a route from vertex A to vertex B in the graph. We show how such a graph can...... of the form: "Is there an edge such that all paths between A and B go via that edge?" and which can quickly be updated when edges are inserted or deleted. We further show how to represent a planar graph such that we can quickly update our representation when an edge is deleted, and such that questions...

  13. Interactive Graph Layout of a Million Nodes

    Directory of Open Access Journals (Sweden)

    Peng Mi

    2016-12-01

    Full Text Available Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.

  14. Profinite graphs and groups

    CERN Document Server

    Ribes, Luis

    2017-01-01

    This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...

  15. Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

    Science.gov (United States)

    Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

    2012-08-01

    We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

  16. An Empirical Comparison of Algorithms to Find Communities in Directed Graphs and Their Application in Web Data Analytics

    DEFF Research Database (Denmark)

    Agreste, Santa; De Meo, Pasquale; Fiumara, Giacomo

    2017-01-01

    Detecting communities in graphs is a fundamental tool to understand the structure of Web-based systems and predict their evolution. Many community detection algorithms are designed to process undirected graphs (i.e., graphs with bidirectional edges) but many graphs on the Web-e.g., microblogging ...... the best trade-off between accuracy and computational performance and, therefore, it has to be considered as a promising tool for Web Data Analytics purposes....

  17. Graph 500 on OpenSHMEM: Using a Practical Survey of Past Work to Motivate Novel Algorithmic Developments

    Energy Technology Data Exchange (ETDEWEB)

    Grossman, Max [Rice Univ., Houston, TX (United States); Pritchard Jr., Howard Porter [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Budimlic, Zoran [Rice Univ., Houston, TX (United States); Sarkar, Vivek [Rice Univ., Houston, TX (United States)

    2016-12-22

    Graph500 [14] is an effort to offer a standardized benchmark across large-scale distributed platforms which captures the behavior of common communicationbound graph algorithms. Graph500 differs from other large-scale benchmarking efforts (such as HPL [6] or HPGMG [7]) primarily in the irregularity of its computation and data access patterns. The core computational kernel of Graph500 is a breadth-first search (BFS) implemented on an undirected graph. The output of Graph500 is a spanning tree of the input graph, usually represented by a predecessor mapping for every node in the graph. The Graph500 benchmark defines several pre-defined input sizes for implementers to test against. This report summarizes investigation into implementing the Graph500 benchmark on OpenSHMEM, and focuses on first building a strong and practical understanding of the strengths and limitations of past work before proposing and developing novel extensions.

  18. Neural complexity: A graph theoretic interpretation

    Science.gov (United States)

    Barnett, L.; Buckley, C. L.; Bullock, S.

    2011-04-01

    One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end, Tononi [Proc. Natl. Acad. Sci. USA.PNASA60027-842410.1073/pnas.91.11.5033 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system’s dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns [Cereb. Cortex53OPAV1047-321110.1093/cercor/10.2.127 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia [Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.71.016114 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular, we explicitly establish a dependency of neural complexity on cyclic graph motifs.

  19. Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data.

    Science.gov (United States)

    Gallant, Andrew; Leiserson, Mark D M; Kachalov, Maxim; Cowen, Lenore J; Hescott, Benjamin J

    2013-01-18

    New technology has resulted in high-throughput screens for pairwise genetic interactions in yeast and other model organisms. For each pair in a collection of non-essential genes, an epistasis score is obtained, representing how much sicker (or healthier) the double-knockout organism will be compared to what would be expected from the sickness of the component single knockouts. Recent algorithmic work has identified graph-theoretic patterns in this data that can indicate functional modules, and even sets of genes that may occur in compensatory pathways, such as a BPM-type schema first introduced by Kelley and Ideker. However, to date, any algorithms for finding such patterns in the data were implemented internally, with no software being made publically available. Genecentric is a new package that implements a parallelized version of the Leiserson et al. algorithm (J Comput Biol 18:1399-1409, 2011) for generating generalized BPMs from high-throughput genetic interaction data. Given a matrix of weighted epistasis values for a set of double knock-outs, Genecentric returns a list of generalized BPMs that may represent compensatory pathways. Genecentric also has an extension, GenecentricGO, to query FuncAssociate (Bioinformatics 25:3043-3044, 2009) to retrieve GO enrichment statistics on generated BPMs. Python is the only dependency, and our web site provides working examples and documentation. We find that Genecentric can be used to find coherent functional and perhaps compensatory gene sets from high throughput genetic interaction data. Genecentric is made freely available for download under the GPLv2 from http://bcb.cs.tufts.edu/genecentric.

  20. Unwinding the hairball graph: Pruning algorithms for weighted complex networks

    Science.gov (United States)

    Dianati, Navid

    2016-01-01

    Empirical networks of weighted dyadic relations often contain "noisy" edges that alter the global characteristics of the network and obfuscate the most important structures therein. Graph pruning is the process of identifying the most significant edges according to a generative null model and extracting the subgraph consisting of those edges. Here, we focus on integer-weighted graphs commonly arising when weights count the occurrences of an "event" relating the nodes. We introduce a simple and intuitive null model related to the configuration model of network generation and derive two significance filters from it: the marginal likelihood filter (MLF) and the global likelihood filter (GLF). The former is a fast algorithm assigning a significance score to each edge based on the marginal distribution of edge weights, whereas the latter is an ensemble approach which takes into account the correlations among edges. We apply these filters to the network of air traffic volume between US airports and recover a geographically faithful representation of the graph. Furthermore, compared with thresholding based on edge weight, we show that our filters extract a larger and significantly sparser giant component.

  1. Information Retrieval and Graph Analysis Approaches for Book Recommendation

    OpenAIRE

    Chahinez Benkoussas; Patrice Bellot

    2015-01-01

    A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval ...

  2. Interactive Graph Layout of a Million Nodes

    OpenAIRE

    Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North

    2016-01-01

    Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...

  3. Dynamic Programming and Graph Algorithms in Computer Vision*

    Science.gov (United States)

    Felzenszwalb, Pedro F.; Zabih, Ramin

    2013-01-01

    Optimization is a powerful paradigm for expressing and solving problems in a wide range of areas, and has been successfully applied to many vision problems. Discrete optimization techniques are especially interesting, since by carefully exploiting problem structure they often provide non-trivial guarantees concerning solution quality. In this paper we briefly review dynamic programming and graph algorithms, and discuss representative examples of how these discrete optimization techniques have been applied to some classical vision problems. We focus on the low-level vision problem of stereo; the mid-level problem of interactive object segmentation; and the high-level problem of model-based recognition. PMID:20660950

  4. MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

    Energy Technology Data Exchange (ETDEWEB)

    Liu, X; Belcher, AH; Wiersma, R [The University of Chicago, Chicago, IL (United States)

    2016-06-15

    Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also

  5. Software for Graph Analysis and Visualization

    Directory of Open Access Journals (Sweden)

    M. I. Kolomeychenko

    2014-01-01

    Full Text Available This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links. Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.

  6. On characterizing terrain visibility graphs

    Directory of Open Access Journals (Sweden)

    William Evans

    2015-06-01

    Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.

  7. Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

    Science.gov (United States)

    Haraldsdóttir, Hulda S.; Fleming, Ronan M. T.

    2016-01-01

    Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties. PMID:27870845

  8. A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

    Science.gov (United States)

    Chen, Jung-Chieh

    This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

  9. The Container Problem in Bubble-Sort Graphs

    Science.gov (United States)

    Suzuki, Yasuto; Kaneko, Keiichi

    Bubble-sort graphs are variants of Cayley graphs. A bubble-sort graph is suitable as a topology for massively parallel systems because of its simple and regular structure. Therefore, in this study, we focus on n-bubble-sort graphs and propose an algorithm to obtain n-1 disjoint paths between two arbitrary nodes in time bounded by a polynomial in n, the degree of the graph plus one. We estimate the time complexity of the algorithm and the sum of the path lengths after proving the correctness of the algorithm. In addition, we report the results of computer experiments evaluating the average performance of the algorithm.

  10. Graph-based clustering and data visualization algorithms

    CERN Document Server

    Vathy-Fogarassy, Ágnes

    2013-01-01

    This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on

  11. Graph embedding with rich information through heterogeneous graph

    KAUST Repository

    Sun, Guolei

    2017-11-12

    Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.

  12. Information Retrieval and Graph Analysis Approaches for Book Recommendation

    Directory of Open Access Journals (Sweden)

    Chahinez Benkoussas

    2015-01-01

    Full Text Available A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

  13. Information Retrieval and Graph Analysis Approaches for Book Recommendation.

    Science.gov (United States)

    Benkoussas, Chahinez; Bellot, Patrice

    2015-01-01

    A combination of multiple information retrieval approaches is proposed for the purpose of book recommendation. In this paper, book recommendation is based on complex user's query. We used different theoretical retrieval models: probabilistic as InL2 (Divergence from Randomness model) and language model and tested their interpolated combination. Graph analysis algorithms such as PageRank have been successful in Web environments. We consider the application of this algorithm in a new retrieval approach to related document network comprised of social links. We called Directed Graph of Documents (DGD) a network constructed with documents and social information provided from each one of them. Specifically, this work tackles the problem of book recommendation in the context of INEX (Initiative for the Evaluation of XML retrieval) Social Book Search track. A series of reranking experiments demonstrate that combining retrieval models yields significant improvements in terms of standard ranked retrieval metrics. These results extend the applicability of link analysis algorithms to different environments.

  14. Quantum information processing with graph states

    International Nuclear Information System (INIS)

    Schlingemann, Dirk-Michael

    2005-04-01

    Graph states are multiparticle states which are associated with graphs. Each vertex of the graph corresponds to a single system or particle. The links describe quantum correlations (entanglement) between pairs of connected particles. Graph states were initiated independently by two research groups: On the one hand, graph states were introduced by Briegel and Raussendorf as a resource for a new model of one-way quantum computing, where algorithms are implemented by a sequence of measurements at single particles. On the other hand, graph states were developed by the author of this thesis and ReinhardWerner in Braunschweig, as a tool to build quantum error correcting codes, called graph codes. The connection between the two approaches was fully realized in close cooperation of both research groups. This habilitation thesis provides a survey of the theory of graph codes, focussing mainly, but not exclusively on the author's own research work. We present the theoretical and mathematical background for the analysis of graph codes. The concept of one-way quantum computing for general graph states is discussed. We explicitly show how to realize the encoding and decoding device of a graph code on a one-way quantum computer. This kind of implementation is to be seen as a mathematical description of a quantum memory device. In addition to that, we investigate interaction processes, which enable the creation of graph states on very large systems. Particular graph states can be created, for instance, by an Ising type interaction between next neighbor particles which sits at the points of an infinitely extended cubic lattice. Based on the theory of quantum cellular automata, we give a constructive characterization of general interactions which create a translationally invariant graph state. (orig.)

  15. Design of application for graph's handling with heuristic algorithms of analysis

    OpenAIRE

    López, Carlos Andrés; Ardila Urueña, William

    2008-01-01

    El siguiente artículo muestra la manera de desarrollar una sencilla aplicación de entorno grafico sobre la cual se puede experimentar diversas técnicas, desde algoritmos de resolución de grafos hasta heurísticas empleadas en inteligencia artificial. The next section shows how to develop a simple graphical application environment on which to experiment with various techniques, from algorithms resolution graph until heuristics used in artificial intelligence.

  16. GoFFish: A Sub-Graph Centric Framework for Large-Scale Graph Analytics1

    Energy Technology Data Exchange (ETDEWEB)

    Simmhan, Yogesh; Kumbhare, Alok; Wickramaarachchi, Charith; Nagarkar, Soonil; Ravi, Santosh; Raghavendra, Cauligi; Prasanna, Viktor

    2014-08-25

    Large scale graph processing is a major research area for Big Data exploration. Vertex centric programming models like Pregel are gaining traction due to their simple abstraction that allows for scalable execution on distributed systems naturally. However, there are limitations to this approach which cause vertex centric algorithms to under-perform due to poor compute to communication overhead ratio and slow convergence of iterative superstep. In this paper we introduce GoFFish a scalable sub-graph centric framework co-designed with a distributed persistent graph storage for large scale graph analytics on commodity clusters. We introduce a sub-graph centric programming abstraction that combines the scalability of a vertex centric approach with the flexibility of shared memory sub-graph computation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation. We map Connected Components, SSSP and PageRank algorithms to this model to illustrate its flexibility. Further, we empirically analyze GoFFish using several real world graphs and demonstrate its significant performance improvement, orders of magnitude in some cases, compared to Apache Giraph, the leading open source vertex centric implementation.

  17. On an edge partition and root graphs of some classes of line graphs

    Directory of Open Access Journals (Sweden)

    K Pravas

    2017-04-01

    Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.

  18. Graph theoretical stable allocation as a tool for reproduction of control by human operators

    Science.gov (United States)

    van Nooijen, Ronald; Ertsen, Maurits; Kolechkina, Alla

    2016-04-01

    During the design of central control algorithms for existing water resource systems under manual control it is important to consider the interaction with parts of the system that remain under manual control and to compare the proposed new system with the existing manual methods. In graph theory the "stable allocation" problem has good solution algorithms and allows for formulation of flow distribution problems in terms of priorities. As a test case for the use of this approach we used the algorithm to derive water allocation rules for the Gezira Scheme, an irrigation system located between the Blue and White Niles south of Khartoum. In 1925, Gezira started with 300,000 acres; currently it covers close to two million acres.

  19. Survey of Approaches to Generate Realistic Synthetic Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Lim, Seung-Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Shankar, Mallikarjun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Imam, Neena [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2016-10-01

    A graph is a flexible data structure that can represent relationships between entities. As with other data analysis tasks, the use of realistic graphs is critical to obtaining valid research results. Unfortunately, using the actual ("real-world") graphs for research and new algorithm development is difficult due to the presence of sensitive information in the data or due to the scale of data. This results in practitioners developing algorithms and systems that employ synthetic graphs instead of real-world graphs. Generating realistic synthetic graphs that provide reliable statistical confidence to algorithmic analysis and system evaluation involves addressing technical hurdles in a broad set of areas. This report surveys the state of the art in approaches to generate realistic graphs that are derived from fitted graph models on real-world graphs.

  20. Query optimization for graph analytics on linked data using SPARQL

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Seokyong [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lee, Sangkeun [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Lim, Seung -Hwan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sukumar, Sreenivas R. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Vatsavai, Ranga Raju [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

    2015-07-01

    Triplestores that support query languages such as SPARQL are emerging as the preferred and scalable solution to represent data and meta-data as massive heterogeneous graphs using Semantic Web standards. With increasing adoption, the desire to conduct graph-theoretic mining and exploratory analysis has also increased. Addressing that desire, this paper presents a solution that is the marriage of Graph Theory and the Semantic Web. We present software that can analyze Linked Data using graph operations such as counting triangles, finding eccentricity, testing connectedness, and computing PageRank directly on triple stores via the SPARQL interface. We describe the process of optimizing performance of the SPARQL-based implementation of such popular graph algorithms by reducing the space-overhead, simplifying iterative complexity and removing redundant computations by understanding query plans. Our optimized approach shows significant performance gains on triplestores hosted on stand-alone workstations as well as hardware-optimized scalable supercomputers such as the Cray XMT.

  1. Efficient Algorithmic Frameworks via Structural Graph Theory

    Science.gov (United States)

    2016-10-28

    constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein

  2. Simplifying Scalable Graph Processing with a Domain-Specific Language

    KAUST Repository

    Hong, Sungpack; Salihoglu, Semih; Widom, Jennifer; Olukotun, Kunle

    2014-01-01

    Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel's programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.

  3. Simplifying Scalable Graph Processing with a Domain-Specific Language

    KAUST Repository

    Hong, Sungpack

    2014-01-01

    Large-scale graph processing, with its massive data sets, requires distributed processing. However, conventional frameworks for distributed graph processing, such as Pregel, use non-traditional programming models that are well-suited for parallelism and scalability but inconvenient for implementing non-trivial graph algorithms. In this paper, we use Green-Marl, a Domain-Specific Language for graph analysis, to intuitively describe graph algorithms and extend its compiler to generate equivalent Pregel implementations. Using the semantic information captured by Green-Marl, the compiler applies a set of transformation rules that convert imperative graph algorithms into Pregel\\'s programming model. Our experiments show that the Pregel programs generated by the Green-Marl compiler perform similarly to manually coded Pregel implementations of the same algorithms. The compiler is even able to generate a Pregel implementation of a complicated graph algorithm for which a manual Pregel implementation is very challenging.

  4. Price competition on graphs

    NARCIS (Netherlands)

    Soetevent, A.R.

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial

  5. The relationship between structural and functional connectivity: graph theoretical analysis of an EEG neural mass model

    NARCIS (Netherlands)

    Ponten, S.C.; Daffertshofer, A.; Hillebrand, A.; Stam, C.J.

    2010-01-01

    We investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram (EEG). Thirty-two neural mass models (NMMs), each representing the lump activity

  6. Graph Mining Meets the Semantic Web

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Lim, Seung-Hwan [ORNL

    2015-01-01

    The Resource Description Framework (RDF) and SPARQL Protocol and RDF Query Language (SPARQL) were introduced about a decade ago to enable flexible schema-free data interchange on the Semantic Web. Today, data scientists use the framework as a scalable graph representation for integrating, querying, exploring and analyzing data sets hosted at different sources. With increasing adoption, the need for graph mining capabilities for the Semantic Web has emerged. We address that need through implementation of three popular iterative Graph Mining algorithms (Triangle count, Connected component analysis, and PageRank). We implement these algorithms as SPARQL queries, wrapped within Python scripts. We evaluate the performance of our implementation on 6 real world data sets and show graph mining algorithms (that have a linear-algebra formulation) can indeed be unleashed on data represented as RDF graphs using the SPARQL query interface.

  7. Reaction factoring and bipartite update graphs accelerate the Gillespie Algorithm for large-scale biochemical systems.

    Science.gov (United States)

    Indurkhya, Sagar; Beal, Jacob

    2010-01-06

    ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models.

  8. Quantum complexity of graph and algebraic problems

    International Nuclear Information System (INIS)

    Doern, Sebastian

    2008-01-01

    This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)

  9. Quantum complexity of graph and algebraic problems

    Energy Technology Data Exchange (ETDEWEB)

    Doern, Sebastian

    2008-02-04

    This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)

  10. The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

    Directory of Open Access Journals (Sweden)

    Unil Yun

    2016-05-01

    Full Text Available Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

  11. Dynamic airspace configuration method based on a weighted graph model

    Directory of Open Access Journals (Sweden)

    Chen Yangzhou

    2014-08-01

    Full Text Available This paper proposes a new method for dynamic airspace configuration based on a weighted graph model. The method begins with the construction of an undirected graph for the given airspace, where the vertices represent those key points such as airports, waypoints, and the edges represent those air routes. Those vertices are used as the sites of Voronoi diagram, which divides the airspace into units called as cells. Then, aircraft counts of both each cell and of each air-route are computed. Thus, by assigning both the vertices and the edges with those aircraft counts, a weighted graph model comes into being. Accordingly the airspace configuration problem is described as a weighted graph partitioning problem. Then, the problem is solved by a graph partitioning algorithm, which is a mixture of general weighted graph cuts algorithm, an optimal dynamic load balancing algorithm and a heuristic algorithm. After the cuts algorithm partitions the model into sub-graphs, the load balancing algorithm together with the heuristic algorithm transfers aircraft counts to balance workload among sub-graphs. Lastly, airspace configuration is completed by determining the sector boundaries. The simulation result shows that the designed sectors satisfy not only workload balancing condition, but also the constraints such as convexity, connectivity, as well as minimum distance constraint.

  12. Graph Theory. 2. Vertex Descriptors and Graph Coloring

    Directory of Open Access Journals (Sweden)

    Lorentz JÄNTSCHI

    2002-12-01

    Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.

  13. Guidelines for a graph-theoretic implementation of structural equation modeling

    Science.gov (United States)

    Grace, James B.; Schoolmaster, Donald R.; Guntenspergen, Glenn R.; Little, Amanda M.; Mitchell, Brian R.; Miller, Kathryn M.; Schweiger, E. William

    2012-01-01

    Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for

  14. Graph-theoretic approach to quantum correlations.

    Science.gov (United States)

    Cabello, Adán; Severini, Simone; Winter, Andreas

    2014-01-31

    Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.

  15. Uniform Single Valued Neutrosophic Graphs

    Directory of Open Access Journals (Sweden)

    S. Broumi

    2017-09-01

    Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

  16. Quantum Graph Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-01-01

    In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.

  17. A study of brain networks associated with swallowing using graph-theoretical approaches.

    Directory of Open Access Journals (Sweden)

    Bo Luan

    Full Text Available Functional connectivity between brain regions during swallowing tasks is still not well understood. Understanding these complex interactions is of great interest from both a scientific and a clinical perspective. In this study, functional magnetic resonance imaging (fMRI was utilized to study brain functional networks during voluntary saliva swallowing in twenty-two adult healthy subjects (all females, [Formula: see text] years of age. To construct these functional connections, we computed mean partial correlation matrices over ninety brain regions for each participant. Two regions were determined to be functionally connected if their correlation was above a certain threshold. These correlation matrices were then analyzed using graph-theoretical approaches. In particular, we considered several network measures for the whole brain and for swallowing-related brain regions. The results have shown that significant pairwise functional connections were, mostly, either local and intra-hemispheric or symmetrically inter-hemispheric. Furthermore, we showed that all human brain functional network, although varying in some degree, had typical small-world properties as compared to regular networks and random networks. These properties allow information transfer within the network at a relatively high efficiency. Swallowing-related brain regions also had higher values for some of the network measures in comparison to when these measures were calculated for the whole brain. The current results warrant further investigation of graph-theoretical approaches as a potential tool for understanding the neural basis of dysphagia.

  18. A Graph Summarization Algorithm Based on RFID Logistics

    Science.gov (United States)

    Sun, Yan; Hu, Kongfa; Lu, Zhipeng; Zhao, Li; Chen, Ling

    Radio Frequency Identification (RFID) applications are set to play an essential role in object tracking and supply chain management systems. The volume of data generated by a typical RFID application will be enormous as each item will generate a complete history of all the individual locations that it occupied at every point in time. The movement trails of such RFID data form gigantic commodity flowgraph representing the locations and durations of the path stages traversed by each item. In this paper, we use graph to construct a warehouse of RFID commodity flows, and introduce a database-style operation to summarize graphs, which produces a summary graph by grouping nodes based on user-selected node attributes, further allows users to control the hierarchy of summaries. It can cut down the size of graphs, and provide convenience for users to study just on the shrunk graph which they interested. Through extensive experiments, we demonstrate the effectiveness and efficiency of the proposed method.

  19. Price Competition on Graphs

    OpenAIRE

    Adriaan R. Soetevent

    2010-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...

  20. Price Competition on Graphs

    OpenAIRE

    Pim Heijnen; Adriaan Soetevent

    2014-01-01

    This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...

  1. Graphs with branchwidth at most three

    NARCIS (Netherlands)

    Bodlaender, H.L.; Thilikos, D.M.

    1997-01-01

    In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph

  2. Multiple graph regularized nonnegative matrix factorization

    KAUST Repository

    Wang, Jim Jing-Yan

    2013-10-01

    Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer\\'s disease diagnosis task demonstrate the effectiveness of the proposed algorithm. © 2013 Elsevier Ltd. All rights reserved.

  3. Graph theoretical analysis of EEG functional connectivity during music perception.

    Science.gov (United States)

    Wu, Junjie; Zhang, Junsong; Liu, Chu; Liu, Dongwei; Ding, Xiaojun; Zhou, Changle

    2012-11-05

    The present study evaluated the effect of music on large-scale structure of functional brain networks using graph theoretical concepts. While most studies on music perception used Western music as an acoustic stimulus, Guqin music, representative of Eastern music, was selected for this experiment to increase our knowledge of music perception. Electroencephalography (EEG) was recorded from non-musician volunteers in three conditions: Guqin music, noise and silence backgrounds. Phase coherence was calculated in the alpha band and between all pairs of EEG channels to construct correlation matrices. Each resulting matrix was converted into a weighted graph using a threshold, and two network measures: the clustering coefficient and characteristic path length were calculated. Music perception was found to display a higher level mean phase coherence. Over the whole range of thresholds, the clustering coefficient was larger while listening to music, whereas the path length was smaller. Networks in music background still had a shorter characteristic path length even after the correction for differences in mean synchronization level among background conditions. This topological change indicated a more optimal structure under music perception. Thus, prominent small-world properties are confirmed in functional brain networks. Furthermore, music perception shows an increase of functional connectivity and an enhancement of small-world network organizations. Copyright © 2012 Elsevier B.V. All rights reserved.

  4. Performance criteria for graph clustering and Markov cluster experiments

    NARCIS (Netherlands)

    S. van Dongen

    2000-01-01

    textabstractIn~[1] a cluster algorithm for graphs was introduced called the Markov cluster algorithm or MCL~algorithm. The algorithm is based on simulation of (stochastic) flow in graphs by means of alternation of two operators, expansion and inflation. The results in~[2] establish an intrinsic

  5. Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks

    Directory of Open Access Journals (Sweden)

    Lindsay eRutter

    2013-07-01

    Full Text Available Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.

  6. Kolmogorov and Zabih’s Graph Cuts Stereo Matching Algorithm

    Directory of Open Access Journals (Sweden)

    Vladimir Kolmogorov

    2014-10-01

    Full Text Available Binocular stereovision estimates the three-dimensional shape of a scene from two photographs taken from different points of view. In rectified epipolar geometry, this is equivalent to a matching problem. This article describes a method proposed by Kolmogorov and Zabih in 2001, which puts forward an energy-based formulation. The aim is to minimize a four-term-energy. This energy is not convex and cannot be minimized except among a class of perturbations called expansion moves, in which case an exact minimization can be done with graph cuts techniques. One noteworthy feature of this method is that it handles occlusion: The algorithm detects points that cannot be matched with any point in the other image. In this method displacements are pixel accurate (no subpixel refinement.

  7. Reaction factoring and bipartite update graphs accelerate the Gillespie Algorithm for large-scale biochemical systems.

    Directory of Open Access Journals (Sweden)

    Sagar Indurkhya

    Full Text Available ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1 a small number of reactions tend to occur a disproportionately large percentage of the time, and (2 a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models.

  8. Reaction Factoring and Bipartite Update Graphs Accelerate the Gillespie Algorithm for Large-Scale Biochemical Systems

    Science.gov (United States)

    Indurkhya, Sagar; Beal, Jacob

    2010-01-01

    ODE simulations of chemical systems perform poorly when some of the species have extremely low concentrations. Stochastic simulation methods, which can handle this case, have been impractical for large systems due to computational complexity. We observe, however, that when modeling complex biological systems: (1) a small number of reactions tend to occur a disproportionately large percentage of the time, and (2) a small number of species tend to participate in a disproportionately large percentage of reactions. We exploit these properties in LOLCAT Method, a new implementation of the Gillespie Algorithm. First, factoring reaction propensities allows many propensities dependent on a single species to be updated in a single operation. Second, representing dependencies between reactions with a bipartite graph of reactions and species requires only storage for reactions, rather than the required for a graph that includes only reactions. Together, these improvements allow our implementation of LOLCAT Method to execute orders of magnitude faster than currently existing Gillespie Algorithm variants when simulating several yeast MAPK cascade models. PMID:20066048

  9. Multiple graph regularized protein domain ranking.

    Science.gov (United States)

    Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

    2012-11-19

    Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

  10. Using neutrosophic graph cut segmentation algorithm for qualified rendering image selection in thyroid elastography video.

    Science.gov (United States)

    Guo, Yanhui; Jiang, Shuang-Quan; Sun, Baiqing; Siuly, Siuly; Şengür, Abdulkadir; Tian, Jia-Wei

    2017-12-01

    Recently, elastography has become very popular in clinical investigation for thyroid cancer detection and diagnosis. In elastogram, the stress results of the thyroid are displayed using pseudo colors. Due to variation of the rendering results in different frames, it is difficult for radiologists to manually select the qualified frame image quickly and efficiently. The purpose of this study is to find the qualified rendering result in the thyroid elastogram. This paper employs an efficient thyroid ultrasound image segmentation algorithm based on neutrosophic graph cut to find the qualified rendering images. Firstly, a thyroid ultrasound image is mapped into neutrosophic set, and an indeterminacy filter is constructed to reduce the indeterminacy of the spatial and intensity information in the image. A graph is defined on the image and the weight for each pixel is represented using the value after indeterminacy filtering. The segmentation results are obtained using a maximum-flow algorithm on the graph. Then the anatomic structure is identified in thyroid ultrasound image. Finally the rendering colors on these anatomic regions are extracted and validated to find the frames which satisfy the selection criteria. To test the performance of the proposed method, a thyroid elastogram dataset is built and totally 33 cases were collected. An experienced radiologist manually evaluates the selection results of the proposed method. Experimental results demonstrate that the proposed method finds the qualified rendering frame with 100% accuracy. The proposed scheme assists the radiologists to diagnose the thyroid diseases using the qualified rendering images.

  11. Recognition of fractal graphs

    NARCIS (Netherlands)

    Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

    1999-01-01

    Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

  12. Impaired cerebral blood flow networks in temporal lobe epilepsy with hippocampal sclerosis: A graph theoretical approach.

    Science.gov (United States)

    Sone, Daichi; Matsuda, Hiroshi; Ota, Miho; Maikusa, Norihide; Kimura, Yukio; Sumida, Kaoru; Yokoyama, Kota; Imabayashi, Etsuko; Watanabe, Masako; Watanabe, Yutaka; Okazaki, Mitsutoshi; Sato, Noriko

    2016-09-01

    Graph theory is an emerging method to investigate brain networks. Altered cerebral blood flow (CBF) has frequently been reported in temporal lobe epilepsy (TLE), but graph theoretical findings of CBF are poorly understood. Here, we explored graph theoretical networks of CBF in TLE using arterial spin labeling imaging. We recruited patients with TLE and unilateral hippocampal sclerosis (HS) (19 patients with left TLE, and 21 with right TLE) and 20 gender- and age-matched healthy control subjects. We obtained all participants' CBF maps using pseudo-continuous arterial spin labeling and analyzed them using the Graph Analysis Toolbox (GAT) software program. As a result, compared to the controls, the patients with left TLE showed a significantly low clustering coefficient (p=0.024), local efficiency (p=0.001), global efficiency (p=0.010), and high transitivity (p=0.015), whereas the patients with right TLE showed significantly high assortativity (p=0.046) and transitivity (p=0.011). The group with right TLE also had high characteristic path length values (p=0.085), low global efficiency (p=0.078), and low resilience to targeted attack (p=0.101) at a trend level. Lower normalized clustering coefficient (p=0.081) in the left TLE and higher normalized characteristic path length (p=0.089) in the right TLE were found also at a trend level. Both the patients with left and right TLE showed significantly decreased clustering in similar areas, i.e., the cingulate gyri, precuneus, and occipital lobe. Our findings revealed differing left-right network metrics in which an inefficient CBF network in left TLE and vulnerability to irritation in right TLE are suggested. The left-right common finding of regional decreased clustering might reflect impaired default-mode networks in TLE. Copyright © 2016 Elsevier Inc. All rights reserved.

  13. Quantitative graph theory mathematical foundations and applications

    CERN Document Server

    Dehmer, Matthias

    2014-01-01

    The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat

  14. A heterogeneous graph-based recommendation simulator

    Energy Technology Data Exchange (ETDEWEB)

    Yeonchan, Ahn [Seoul National University; Sungchan, Park [Seoul National University; Lee, Matt Sangkeun [ORNL; Sang-goo, Lee [Seoul National University

    2013-01-01

    Heterogeneous graph-based recommendation frameworks have flexibility in that they can incorporate various recommendation algorithms and various kinds of information to produce better results. In this demonstration, we present a heterogeneous graph-based recommendation simulator which enables participants to experience the flexibility of a heterogeneous graph-based recommendation method. With our system, participants can simulate various recommendation semantics by expressing the semantics via meaningful paths like User Movie User Movie. The simulator then returns the recommendation results on the fly based on the user-customized semantics using a fast Monte Carlo algorithm.

  15. The STAPL Parallel Graph Library

    KAUST Repository

    Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence

    2013-01-01

    This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable

  16. Theoretical analysis of two ACO approaches for the traveling salesman problem

    DEFF Research Database (Denmark)

    Kötzing, Timo; Neumann, Frank; Röglin, Heiko

    2012-01-01

    Bioinspired algorithms, such as evolutionary algorithms and ant colony optimization, are widely used for different combinatorial optimization problems. These algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. This paper contributes...... to the theoretical analysis of ant colony optimization and studies this type of algorithm on one of the most prominent combinatorial optimization problems, namely the traveling salesperson problem (TSP). We present a new construction graph and show that it has a stronger local property than one commonly used...... for constructing solutions of the TSP. The rigorous runtime analysis for two ant colony optimization algorithms, based on these two construction procedures, shows that they lead to good approximation in expected polynomial time on random instances. Furthermore, we point out in which situations our algorithms get...

  17. A NEW HYBRID GENETIC ALGORITHM FOR VERTEX COVER PROBLEM

    OpenAIRE

    UĞURLU, Onur

    2015-01-01

    The minimum vertex cover  problem belongs to the  class  of  NP-compl ete  graph  theoretical problems. This paper presents a hybrid genetic algorithm to solve minimum ver tex cover problem. In this paper, it has been shown that when local optimization technique is added t o genetic algorithm to form hybrid genetic algorithm, it gives more quality solution than simple genet ic algorithm. Also, anew mutation operator has been developed especially for minimum verte...

  18. Multiple graph regularized protein domain ranking

    KAUST Repository

    Wang, Jim Jing-Yan

    2012-11-19

    Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

  19. Multiple graph regularized protein domain ranking

    KAUST Repository

    Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

    2012-01-01

    Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.

  20. Multiple graph regularized protein domain ranking

    Directory of Open Access Journals (Sweden)

    Wang Jim

    2012-11-01

    Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.

  1. Groupies in multitype random graphs

    OpenAIRE

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  2. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  3. A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

    International Nuclear Information System (INIS)

    Bedini, Andrea; Jacobsen, Jesper Lykke

    2010-01-01

    Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N = 100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ∼ exp(1.516√N), a substantial improvement over the exponential running time ∼exp (0.245N) provided by the hitherto best-known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.

  4. Graph Regularized Auto-Encoders for Image Representation.

    Science.gov (United States)

    Yiyi Liao; Yue Wang; Yong Liu

    2017-06-01

    Image representation has been intensively explored in the domain of computer vision for its significant influence on the relative tasks such as image clustering and classification. It is valuable to learn a low-dimensional representation of an image which preserves its inherent information from the original image space. At the perspective of manifold learning, this is implemented with the local invariant idea to capture the intrinsic low-dimensional manifold embedded in the high-dimensional input space. Inspired by the recent successes of deep architectures, we propose a local invariant deep nonlinear mapping algorithm, called graph regularized auto-encoder (GAE). With the graph regularization, the proposed method preserves the local connectivity from the original image space to the representation space, while the stacked auto-encoders provide explicit encoding model for fast inference and powerful expressive capacity for complex modeling. Theoretical analysis shows that the graph regularizer penalizes the weighted Frobenius norm of the Jacobian matrix of the encoder mapping, where the weight matrix captures the local property in the input space. Furthermore, the underlying effects on the hidden representation space are revealed, providing insightful explanation to the advantage of the proposed method. Finally, the experimental results on both clustering and classification tasks demonstrate the effectiveness of our GAE as well as the correctness of the proposed theoretical analysis, and it also suggests that GAE is a superior solution to the current deep representation learning techniques comparing with variant auto-encoders and existing local invariant methods.

  5. Coloring geographical threshold graphs

    Energy Technology Data Exchange (ETDEWEB)

    Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH

    2008-01-01

    We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.

  6. On the Organization of Parallel Operation of Some Algorithms for Finding the Shortest Path on a Graph on a Computer System with Multiple Instruction Stream and Single Data Stream

    Directory of Open Access Journals (Sweden)

    V. E. Podol'skii

    2015-01-01

    Full Text Available The paper considers the implementing Bellman-Ford and Lee algorithms to find the shortest graph path on a computer system with multiple instruction stream and single data stream (MISD. The MISD computer is a computer that executes commands of arithmetic-logical processing (on the CPU and commands of structures processing (on the structures processor in parallel on a single data stream. Transformation of sequential programs into the MISD programs is a labor intensity process because it requires a stream of the arithmetic-logical processing to be manually separated from that of the structures processing. Algorithms based on the processing of data structures (e.g., algorithms on graphs show high performance on a MISD computer. Bellman-Ford and Lee algorithms for finding the shortest path on a graph are representatives of these algorithms. They are applied to robotics for automatic planning of the robot movement in-situ. Modification of Bellman-Ford and Lee algorithms for finding the shortest graph path in coprocessor MISD mode and the parallel MISD modification of these algorithms were first obtained in this article. Thus, this article continues a series of studies on the transformation of sequential algorithms into MISD ones (Dijkstra and Ford-Fulkerson 's algorithms and has a pronouncedly applied nature. The article also presents the analysis results of Bellman-Ford and Lee algorithms in MISD mode. The paper formulates the basic trends of a technique for parallelization of algorithms into arithmetic-logical processing stream and structures processing stream. Among the key areas for future research, development of the mathematical approach to provide a subsequently formalized and automated process of parallelizing sequential algorithms between the CPU and structures processor is highlighted. Among the mathematical models that can be used in future studies there are graph models of algorithms (e.g., dependency graph of a program. Due to the high

  7. TrajGraph: A Graph-Based Visual Analytics Approach to Studying Urban Network Centralities Using Taxi Trajectory Data.

    Science.gov (United States)

    Huang, Xiaoke; Zhao, Ye; Yang, Jing; Zhang, Chong; Ma, Chao; Ye, Xinyue

    2016-01-01

    We propose TrajGraph, a new visual analytics method, for studying urban mobility patterns by integrating graph modeling and visual analysis with taxi trajectory data. A special graph is created to store and manifest real traffic information recorded by taxi trajectories over city streets. It conveys urban transportation dynamics which can be discovered by applying graph analysis algorithms. To support interactive, multiscale visual analytics, a graph partitioning algorithm is applied to create region-level graphs which have smaller size than the original street-level graph. Graph centralities, including Pagerank and betweenness, are computed to characterize the time-varying importance of different urban regions. The centralities are visualized by three coordinated views including a node-link graph view, a map view and a temporal information view. Users can interactively examine the importance of streets to discover and assess city traffic patterns. We have implemented a fully working prototype of this approach and evaluated it using massive taxi trajectories of Shenzhen, China. TrajGraph's capability in revealing the importance of city streets was evaluated by comparing the calculated centralities with the subjective evaluations from a group of drivers in Shenzhen. Feedback from a domain expert was collected. The effectiveness of the visual interface was evaluated through a formal user study. We also present several examples and a case study to demonstrate the usefulness of TrajGraph in urban transportation analysis.

  8. Low-Rank Matrix Factorization With Adaptive Graph Regularizer.

    Science.gov (United States)

    Lu, Gui-Fu; Wang, Yong; Zou, Jian

    2016-05-01

    In this paper, we present a novel low-rank matrix factorization algorithm with adaptive graph regularizer (LMFAGR). We extend the recently proposed low-rank matrix with manifold regularization (MMF) method with an adaptive regularizer. Different from MMF, which constructs an affinity graph in advance, LMFAGR can simultaneously seek graph weight matrix and low-dimensional representations of data. That is, graph construction and low-rank matrix factorization are incorporated into a unified framework, which results in an automatically updated graph rather than a predefined one. The experimental results on some data sets demonstrate that the proposed algorithm outperforms the state-of-the-art low-rank matrix factorization methods.

  9. Computing paths and cycles in biological interaction graphs

    Directory of Open Access Journals (Sweden)

    von Kamp Axel

    2009-06-01

    Full Text Available Abstract Background Interaction graphs (signed directed graphs provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments. Results We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops. Conclusion The calculation of shortest positive

  10. Graph Sampling for Covariance Estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2017-01-01

    specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non

  11. Groupies in multitype random graphs.

    Science.gov (United States)

    Shang, Yilun

    2016-01-01

    A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

  12. Connectivity: Performance Portable Algorithms for graph connectivity v. 0.1

    Energy Technology Data Exchange (ETDEWEB)

    2017-09-21

    Graphs occur in several places in real world from road networks, social networks and scientific simulations. Connectivity is a graph analysis software to graph connectivity in modern architectures like multicore CPUs, Xeon Phi and GPUs.

  13. Graph Creation, Visualisation and Transformation

    Directory of Open Access Journals (Sweden)

    Maribel Fernández

    2010-03-01

    Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.

  14. A seminar on graph theory

    CERN Document Server

    Harary, Frank

    2015-01-01

    Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc

  15. A faithful functor among algebras and graphs

    OpenAIRE

    Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)

    2016-01-01

    The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.

  16. Graph theoretical analysis and application of fMRI-based brain network in Alzheimer's disease

    Directory of Open Access Journals (Sweden)

    LIU Xue-na

    2012-08-01

    Full Text Available Alzheimer's disease (AD, a progressive neurodegenerative disease, is clinically characterized by impaired memory and many other cognitive functions. However, the pathophysiological mechanisms underlying the disease are not thoroughly understood. In recent years, using functional magnetic resonance imaging (fMRI as well as advanced graph theory based network analysis approach, several studies of patients with AD suggested abnormal topological organization in both global and regional properties of functional brain networks, specifically, as demonstrated by a loss of small-world network characteristics. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis. In this paper we introduce the essential concepts of complex brain networks theory, and review recent advances of the study on human functional brain networks in AD, especially focusing on the graph theoretical analysis of small-world network based on fMRI. We also propound the existent problems and research orientation.

  17. Bladder segmentation in MR images with watershed segmentation and graph cut algorithm

    Science.gov (United States)

    Blaffert, Thomas; Renisch, Steffen; Schadewaldt, Nicole; Schulz, Heinrich; Wiemker, Rafael

    2014-03-01

    Prostate and cervix cancer diagnosis and treatment planning that is based on MR images benefit from superior soft tissue contrast compared to CT images. For these images an automatic delineation of the prostate or cervix and the organs at risk such as the bladder is highly desirable. This paper describes a method for bladder segmentation that is based on a watershed transform on high image gradient values and gray value valleys together with the classification of watershed regions into bladder contents and tissue by a graph cut algorithm. The obtained results are superior if compared to a simple region-after-region classification.

  18. Theoretic derivation of directed acyclic subgraph algorithm and comparisons with message passing algorithm

    Science.gov (United States)

    Ha, Jeongmok; Jeong, Hong

    2016-07-01

    This study investigates the directed acyclic subgraph (DAS) algorithm, which is used to solve discrete labeling problems much more rapidly than other Markov-random-field-based inference methods but at a competitive accuracy. However, the mechanism by which the DAS algorithm simultaneously achieves competitive accuracy and fast execution speed, has not been elucidated by a theoretical derivation. We analyze the DAS algorithm by comparing it with a message passing algorithm. Graphical models, inference methods, and energy-minimization frameworks are compared between DAS and message passing algorithms. Moreover, the performances of DAS and other message passing methods [sum-product belief propagation (BP), max-product BP, and tree-reweighted message passing] are experimentally compared.

  19. Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

    Science.gov (United States)

    Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

    2017-12-01

    Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

  20. Transduction on Directed Graphs via Absorbing Random Walks.

    Science.gov (United States)

    De, Jaydeep; Zhang, Xiaowei; Lin, Feng; Cheng, Li

    2017-08-11

    In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications.Different from existing research efforts that either only deal with undirected graphs or circumvent directionality by means of symmetrization, we propose a novel random walk approach on directed graphs using absorbing Markov chains, which can be regarded as maximizing the accumulated expected number of visits from the unlabeled transient states. Our algorithm is simple, easy to implement, and works with large-scale graphs on binary, multiclass, and multi-label prediction problems. Moreover, it is capable of preserving the graph structure even when the input graph is sparse and changes over time, as well as retaining weak signals presented in the directed edges. We present its intimate connections to a number of existing methods, including graph kernels, graph Laplacian based methods, and interestingly, spanning forest of graphs. Its computational complexity and the generalization error are also studied. Empirically our algorithm is systematically evaluated on a wide range of applications, where it has shown to perform competitively comparing to a suite of state-of-the-art methods. In particular, our algorithm is shown to work exceptionally well with large sparse directed graphs with e.g. millions of nodes and tens of millions of edges, where it significantly outperforms other state-of-the-art methods. In the dynamic graph setting involving insertion or deletion of nodes and edge-weight changes over time, it also allows efficient online updates that produce the same results as of the batch update counterparts.

  1. spa: Semi-Supervised Semi-Parametric Graph-Based Estimation in R

    Directory of Open Access Journals (Sweden)

    Mark Culp

    2011-04-01

    Full Text Available In this paper, we present an R package that combines feature-based (X data and graph-based (G data for prediction of the response Y . In this particular case, Y is observed for a subset of the observations (labeled and missing for the remainder (unlabeled. We examine an approach for fitting Y = Xβ + f(G where β is a coefficient vector and f is a function over the vertices of the graph. The procedure is semi-supervised in nature (trained on the labeled and unlabeled sets, requiring iterative algorithms for fitting this estimate. The package provides several key functions for fitting and evaluating an estimator of this type. The package is illustrated on a text analysis data set, where the observations are text documents (papers, the response is the category of paper (either applied or theoretical statistics, the X information is the name of the journal in which the paper resides, and the graph is a co-citation network, with each vertex an observation and each edge the number of times that the two papers cite a common paper. An application involving classification of protein location using a protein interaction graph and an application involving classification on a manifold with part of the feature data converted to a graph are also presented.

  2. Dynamic planar embeddings of dynamic graphs

    DEFF Research Database (Denmark)

    Holm, Jacob; Rotenberg, Eva

    2017-01-01

    query, one-flip- linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We support all updates and queries in O(log 2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler......, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common...

  3. On the Recognition of Fuzzy Circular Interval Graphs

    OpenAIRE

    Oriolo, Gianpaolo; Pietropaoli, Ugo; Stauffer, Gautier

    2011-01-01

    Fuzzy circular interval graphs are a generalization of proper circular arc graphs and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free graphs. In this paper, we provide a polynomial-time algorithm for recognizing such graphs, and more importantly for building a suitable representation.

  4. A New Augmentation Based Algorithm for Extracting Maximal Chordal Subgraphs.

    Science.gov (United States)

    Bhowmick, Sanjukta; Chen, Tzu-Yi; Halappanavar, Mahantesh

    2015-02-01

    A graph is chordal if every cycle of length greater than three contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms' parallelizability. In this paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. We experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.

  5. Minimum nonuniform graph partitioning with unrelated weights

    Science.gov (United States)

    Makarychev, K. S.; Makarychev, Yu S.

    2017-12-01

    We give a bi-criteria approximation algorithm for the Minimum Nonuniform Graph Partitioning problem, recently introduced by Krauthgamer, Naor, Schwartz and Talwar. In this problem, we are given a graph G=(V,E) and k numbers ρ_1,\\dots, ρ_k. The goal is to partition V into k disjoint sets (bins) P_1,\\dots, P_k satisfying \\vert P_i\\vert≤ ρi \\vert V\\vert for all i, so as to minimize the number of edges cut by the partition. Our bi-criteria algorithm gives an O(\\sqrt{log \\vert V\\vert log k}) approximation for the objective function in general graphs and an O(1) approximation in graphs excluding a fixed minor. The approximate solution satisfies the relaxed capacity constraints \\vert P_i\\vert ≤ (5+ \\varepsilon)ρi \\vert V\\vert. This algorithm is an improvement upon the O(log \\vert V\\vert)-approximation algorithm by Krauthgamer, Naor, Schwartz and Talwar. We extend our results to the case of 'unrelated weights' and to the case of 'unrelated d-dimensional weights'. A preliminary version of this work was presented at the 41st International Colloquium on Automata, Languages and Programming (ICALP 2014). Bibliography: 7 titles.

  6. EmptyHeaded: A Relational Engine for Graph Processing.

    Science.gov (United States)

    Aberger, Christopher R; Tu, Susan; Olukotun, Kunle; Ré, Christopher

    2016-01-01

    There are two types of high-performance graph processing engines: low- and high-level engines. Low-level engines (Galois, PowerGraph, Snap) provide optimized data structures and computation models but require users to write low-level imperative code, hence ensuring that efficiency is the burden of the user. In high-level engines, users write in query languages like datalog (SociaLite) or SQL (Grail). High-level engines are easier to use but are orders of magnitude slower than the low-level graph engines. We present EmptyHeaded, a high-level engine that supports a rich datalog-like query language and achieves performance comparable to that of low-level engines. At the core of EmptyHeaded's design is a new class of join algorithms that satisfy strong theoretical guarantees but have thus far not achieved performance comparable to that of specialized graph processing engines. To achieve high performance, EmptyHeaded introduces a new join engine architecture, including a novel query optimizer and data layouts that leverage single-instruction multiple data (SIMD) parallelism. With this architecture, EmptyHeaded outperforms high-level approaches by up to three orders of magnitude on graph pattern queries, PageRank, and Single-Source Shortest Paths (SSSP) and is an order of magnitude faster than many low-level baselines. We validate that EmptyHeaded competes with the best-of-breed low-level engine (Galois), achieving comparable performance on PageRank and at most 3× worse performance on SSSP.

  7. Solved and unsolved problems of chemical graph theory

    International Nuclear Information System (INIS)

    Trinajstic, N.; Klein, D.J.; Randic, M.

    1986-01-01

    The development of several novel graph theoretical concepts and their applications in different branches of chemistry are reviewed. After a few introductory remarks they follow with an outline of selected important graph theoretical invariants, introducing some new results and indicating some open problems. They continue with discussing the problem of graph characterization and construction of graphs of chemical interest, with a particular emphasis on large systems. Finally they consider various problems and difficulties associated with special subgraphs, including subgraphs representing Kekule valence structures. The paper ends with a brief review of structure-property and structure-activity correlations, the topic which is one of prime motivations for application of graph theory to chemistry

  8. GraphAlignment: Bayesian pairwise alignment of biological networks

    Directory of Open Access Journals (Sweden)

    Kolář Michal

    2012-11-01

    Full Text Available Abstract Background With increased experimental availability and accuracy of bio-molecular networks, tools for their comparative and evolutionary analysis are needed. A key component for such studies is the alignment of networks. Results We introduce the Bioconductor package GraphAlignment for pairwise alignment of bio-molecular networks. The alignment incorporates information both from network vertices and network edges and is based on an explicit evolutionary model, allowing inference of all scoring parameters directly from empirical data. We compare the performance of our algorithm to an alternative algorithm, Græmlin 2.0. On simulated data, GraphAlignment outperforms Græmlin 2.0 in several benchmarks except for computational complexity. When there is little or no noise in the data, GraphAlignment is slower than Græmlin 2.0. It is faster than Græmlin 2.0 when processing noisy data containing spurious vertex associations. Its typical case complexity grows approximately as O(N2.6. On empirical bacterial protein-protein interaction networks (PIN and gene co-expression networks, GraphAlignment outperforms Græmlin 2.0 with respect to coverage and specificity, albeit by a small margin. On large eukaryotic PIN, Græmlin 2.0 outperforms GraphAlignment. Conclusions The GraphAlignment algorithm is robust to spurious vertex associations, correctly resolves paralogs, and shows very good performance in identification of homologous vertices defined by high vertex and/or interaction similarity. The simplicity and generality of GraphAlignment edge scoring makes the algorithm an appropriate choice for global alignment of networks.

  9. Quantum snake walk on graphs

    International Nuclear Information System (INIS)

    Rosmanis, Ansis

    2011-01-01

    I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.

  10. Incremental View Maintenance for Deductive Graph Databases Using Generalized Discrimination Networks

    Directory of Open Access Journals (Sweden)

    Thomas Beyhl

    2016-12-01

    Full Text Available Nowadays, graph databases are employed when relationships between entities are in the scope of database queries to avoid performance-critical join operations of relational databases. Graph queries are used to query and modify graphs stored in graph databases. Graph queries employ graph pattern matching that is NP-complete for subgraph isomorphism. Graph database views can be employed that keep ready answers in terms of precalculated graph pattern matches for often stated and complex graph queries to increase query performance. However, such graph database views must be kept consistent with the graphs stored in the graph database. In this paper, we describe how to use incremental graph pattern matching as technique for maintaining graph database views. We present an incremental maintenance algorithm for graph database views, which works for imperatively and declaratively specified graph queries. The evaluation shows that our maintenance algorithm scales when the number of nodes and edges stored in the graph database increases. Furthermore, our evaluation shows that our approach can outperform existing approaches for the incremental maintenance of graph query results.

  11. Dynamic planar embeddings of dynamic graphs

    DEFF Research Database (Denmark)

    Holm, Jacob; Rotenberg, Eva

    2015-01-01

    -flip-linkable(u, v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler, exploiting...... that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour....

  12. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif

    2017-01-07

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  13. Large-Scale Graph Processing Using Apache Giraph

    KAUST Repository

    Sakr, Sherif; Orakzai, Faisal Moeen; Abdelaziz, Ibrahim; Khayyat, Zuhair

    2017-01-01

    This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms.

  14. Stability notions in synthetic graph generation: a preliminary study

    NARCIS (Netherlands)

    van Leeuwen, W.; Fletcher, G.H.L.; Yakovets, N.; Bonifati, A.; Markl, Volker; Orlando, Salvatore; Mitschang, Bernhard

    2017-01-01

    With the rise in adoption of massive graph data, it be- comes increasingly important to design graph processing algorithms which have predictable behavior as the graph scales. This work presents an initial study of stability in the context of a schema-driven synthetic graph generation. Specifically,

  15. An Association-Oriented Partitioning Approach for Streaming Graph Query

    Directory of Open Access Journals (Sweden)

    Yun Hao

    2017-01-01

    Full Text Available The volumes of real-world graphs like knowledge graph are increasing rapidly, which makes streaming graph processing a hot research area. Processing graphs in streaming setting poses significant challenges from different perspectives, among which graph partitioning method plays a key role. Regarding graph query, a well-designed partitioning method is essential for achieving better performance. Existing offline graph partitioning methods often require full knowledge of the graph, which is not possible during streaming graph processing. In order to handle this problem, we propose an association-oriented streaming graph partitioning method named Assc. This approach first computes the rank values of vertices with a hybrid approximate PageRank algorithm. After splitting these vertices with an adapted variant affinity propagation algorithm, the process order on vertices in the sliding window can be determined. Finally, according to the level of these vertices and their association, the partition where the vertices should be distributed is decided. We compare its performance with a set of streaming graph partition methods and METIS, a widely adopted offline approach. The results show that our solution can partition graphs with hundreds of millions of vertices in streaming setting on a large collection of graph datasets and our approach outperforms other graph partitioning methods.

  16. Gossip Consensus Algorithm Based on Time-Varying Influence Factors and Weakly Connected Graph for Opinion Evolution in Social Networks

    Directory of Open Access Journals (Sweden)

    Lingyun Li

    2013-01-01

    Full Text Available We provide a new gossip algorithm to investigate the problem of opinion consensus with the time-varying influence factors and weakly connected graph among multiple agents. What is more, we discuss not only the effect of the time-varying factors and the randomized topological structure but also the spread of misinformation and communication constrains described by probabilistic quantized communication in the social network. Under the underlying weakly connected graph, we first denote that all opinion states converge to a stochastic consensus almost surely; that is, our algorithm indeed achieves the consensus with probability one. Furthermore, our results show that the mean of all the opinion states converges to the average of the initial states when time-varying influence factors satisfy some conditions. Finally, we give a result about the square mean error between the dynamic opinion states and the benchmark without quantized communication.

  17. Finding shortest non-trivial cycles in directed graphs on surfaces

    Directory of Open Access Journals (Sweden)

    Sergio Cabello

    2016-04-01

    Full Text Available Let $D$ be a weighted directed graph cellularly embedded in a surface of genus $g$, orientable or not, possibly with boundary.  We describe algorithms to compute shortest non-contractible and shortest surface non-separating cycles in $D$, generalizing previous results that dealt with undirected graphs.Our first algorithm computes such cycles in $O(n^2\\log n$ time, where $n$ is the total number of vertices and edges of $D$, thus matching the complexity of the best general algorithm in the undirected case.  It revisits and extends Thomassen's 3-path condition; the technique applies to other families of cycles as well.We also provide more efficient algorithms in special cases, such as graphs with small genus or bounded treewidth, using a divide-and-conquer technique that simplifies the graph while preserving the topological properties of its cycles.  Finally, we give an efficient output-sensitive algorithm, whose running time depends on the length of the shortest non-contractible or non-separating cycle.

  18. Subsampling for graph power spectrum estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar; Leus, Geert

    2016-01-01

    In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

  19. Subsampling for graph power spectrum estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar

    2016-10-06

    In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.

  20. Application-Specific Graph Sampling for Frequent Subgraph Mining and Community Detection

    Energy Technology Data Exchange (ETDEWEB)

    Purohit, Sumit; Choudhury, Sutanay; Holder, Lawrence B.

    2017-12-11

    Graph mining is an important data analysis methodology, but struggles as the input graph size increases. The scalability and usability challenges posed by such large graphs make it imperative to sample the input graph and reduce its size. The critical challenge in sampling is to identify the appropriate algorithm to insure the resulting analysis does not suffer heavily from the data reduction. Predicting the expected performance degradation for a given graph and sampling algorithm is also useful. In this paper, we present different sampling approaches for graph mining applications such as Frequent Subgrpah Mining (FSM), and Community Detection (CD). We explore graph metrics such as PageRank, Triangles, and Diversity to sample a graph and conclude that for heterogeneous graphs Triangles and Diversity perform better than degree based metrics. We also present two new sampling variations for targeted graph mining applications. We present empirical results to show that knowledge of the target application, along with input graph properties can be used to select the best sampling algorithm. We also conclude that performance degradation is an abrupt, rather than gradual phenomena, as the sample size decreases. We present the empirical results to show that the performance degradation follows a logistic function.

  1. Genetic Algorithm and Graph Theory Based Matrix Factorization Method for Online Friend Recommendation

    Directory of Open Access Journals (Sweden)

    Qu Li

    2014-01-01

    Full Text Available Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

  2. Declarative Process Mining for DCR Graphs

    DEFF Research Database (Denmark)

    Debois, Søren; Hildebrandt, Thomas T.; Laursen, Paw Høvsgaard

    2017-01-01

    We investigate process mining for the declarative Dynamic Condition Response (DCR) graphs process modelling language. We contribute (a) a process mining algorithm for DCR graphs, (b) a proposal for a set of metrics quantifying output model quality, and (c) a preliminary example-based comparison...

  3. A Clustering Graph Generator

    Energy Technology Data Exchange (ETDEWEB)

    Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-10-26

    In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.

  4. Graph-based semi-supervised learning

    CERN Document Server

    Subramanya, Amarnag

    2014-01-01

    While labeled data is expensive to prepare, ever increasing amounts of unlabeled data is becoming widely available. In order to adapt to this phenomenon, several semi-supervised learning (SSL) algorithms, which learn from labeled as well as unlabeled data, have been developed. In a separate line of work, researchers have started to realize that graphs provide a natural way to represent data in a variety of domains. Graph-based SSL algorithms, which bring together these two lines of work, have been shown to outperform the state-of-the-art in many applications in speech processing, computer visi

  5. Graph Theory to Pure Mathematics: Some Illustrative Examples

    Indian Academy of Sciences (India)

    Graph Theory to Pure Mathematics: Some. Illustrative Examples v Yegnanarayanan is a. Professor of Mathematics at MNM Jain Engineering. College, Chennai. His research interests include graph theory and its applications to both pure maths and theoretical computer science. Keywords. Graph theory, matching theory,.

  6. Overlapping community detection based on link graph using distance dynamics

    Science.gov (United States)

    Chen, Lei; Zhang, Jing; Cai, Li-Jun

    2018-01-01

    The distance dynamics model was recently proposed to detect the disjoint community of a complex network. To identify the overlapping structure of a network using the distance dynamics model, an overlapping community detection algorithm, called L-Attractor, is proposed in this paper. The process of L-Attractor mainly consists of three phases. In the first phase, L-Attractor transforms the original graph to a link graph (a new edge graph) to assure that one node has multiple distances. In the second phase, using the improved distance dynamics model, a dynamic interaction process is introduced to simulate the distance dynamics (shrink or stretch). Through the dynamic interaction process, all distances converge, and the disjoint community structure of the link graph naturally manifests itself. In the third phase, a recovery method is designed to convert the disjoint community structure of the link graph to the overlapping community structure of the original graph. Extensive experiments are conducted on the LFR benchmark networks as well as real-world networks. Based on the results, our algorithm demonstrates higher accuracy and quality than other state-of-the-art algorithms.

  7. Analysis of the Usage of Magnetic Force-directed Approach and Visual Techniques for Interactive Context-based Drawing of Multi-attributed Graphs

    Directory of Open Access Journals (Sweden)

    Zabiniako Vitaly

    2014-12-01

    Full Text Available In this article, the authors perform an analysis in order to assess adaptation of magnetic force-directed algorithms for context-based information extraction from multi-attributed graphs during visualization sessions. Theoretic standings behind magnetic force-directed approach are stated together with review on how particular features of respective algorithms in combination with appropriate visual techniques are especially suitable for improved processing and presenting of knowledge that is captured in form of graphs. The complexity of retrieving multi-attributed information within the proposed approach is handled with dedicated tools, such as selective attraction of nodes to MFE (Magnetic Force Emitter based on search criteria, localization of POI (Point of Interest regions, graph node anchoring, etc. Implicit compatibility of aforementioned tools with interactive nature of data exploration is distinguished. Description of case study, based on bibliometric network analysis is given, which is followed by the review of existing related works in this field. Conclusions are made and further studies in the field of visualization of multi-attributed graphs are defined.

  8. An algorithm for finding a similar subgraph of all Hamiltonian cycles

    Science.gov (United States)

    Wafdan, R.; Ihsan, M.; Suhaimi, D.

    2018-01-01

    This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.

  9. Multi-label literature classification based on the Gene Ontology graph

    Directory of Open Access Journals (Sweden)

    Lu Xinghua

    2008-12-01

    Full Text Available Abstract Background The Gene Ontology is a controlled vocabulary for representing knowledge related to genes and proteins in a computable form. The current effort of manually annotating proteins with the Gene Ontology is outpaced by the rate of accumulation of biomedical knowledge in literature, which urges the development of text mining approaches to facilitate the process by automatically extracting the Gene Ontology annotation from literature. The task is usually cast as a text classification problem, and contemporary methods are confronted with unbalanced training data and the difficulties associated with multi-label classification. Results In this research, we investigated the methods of enhancing automatic multi-label classification of biomedical literature by utilizing the structure of the Gene Ontology graph. We have studied three graph-based multi-label classification algorithms, including a novel stochastic algorithm and two top-down hierarchical classification methods for multi-label literature classification. We systematically evaluated and compared these graph-based classification algorithms to a conventional flat multi-label algorithm. The results indicate that, through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods can significantly improve predictions of the Gene Ontology terms implied by the analyzed text. Furthermore, the graph-based multi-label classifiers are capable of suggesting Gene Ontology annotations (to curators that are closely related to the true annotations even if they fail to predict the true ones directly. A software package implementing the studied algorithms is available for the research community. Conclusion Through utilizing the information from the structure of the Gene Ontology graph, the graph-based multi-label classification methods have better potential than the conventional flat multi-label classification approach to facilitate

  10. Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

    KAUST Repository

    Xu, Zhiqiang

    2017-02-16

    Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

  11. Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

    KAUST Repository

    Xu, Zhiqiang; Cheng, James; Xiao, Xiaokui; Fujimaki, Ryohei; Muraoka, Yusuke

    2017-01-01

    Attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

  12. Intraplate seismicity in Canada: a graph theoretic approach to data analysis and interpretation

    Directory of Open Access Journals (Sweden)

    K. Vasudevan

    2010-10-01

    Full Text Available Intraplate seismicity occurs in central and northern Canada, but the underlying origin and dynamics remain poorly understood. Here, we apply a graph theoretic approach to characterize the statistical structure of spatiotemporal clustering exhibited by intraplate seismicity, a direct consequence of the underlying nonlinear dynamics. Using a recently proposed definition of "recurrences" based on record breaking processes (Davidsen et al., 2006, 2008, we have constructed directed graphs using catalogue data for three selected regions (Region 1: 45°−48° N/74°−80° W; Region 2: 51°−55° N/77°−83° W; and Region 3: 56°−70° N/65°−95° W, with attributes drawn from the location, origin time and the magnitude of the events. Based on comparisons with a null model derived from Poisson distribution or Monte Carlo shuffling of the catalogue data, our results provide strong evidence in support of spatiotemporal correlations of seismicity in all three regions considered. Similar evidence for spatiotemporal clustering has been documented using seismicity catalogues for southern California, suggesting possible similarities in underlying earthquake dynamics of both regions despite huge differences in the variability of seismic activity.

  13. A local search for a graph clustering problem

    Science.gov (United States)

    Navrotskaya, Anna; Il'ev, Victor

    2016-10-01

    In the clustering problems one has to partition a given set of objects (a data set) into some subsets (called clusters) taking into consideration only similarity of the objects. One of most visual formalizations of clustering is graph clustering, that is grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects. In the graph k-clustering problem the number of clusters does not exceed k and the goal is to minimize the number of edges between clusters and the number of missing edges within clusters. This problem is NP-hard for any k ≥ 2. We propose a polynomial time (2k-1)-approximation algorithm for graph k-clustering. Then we apply a local search procedure to the feasible solution found by this algorithm and hold experimental research of obtained heuristics.

  14. Approximating centrality in evolving graphs: toward sublinearity

    Science.gov (United States)

    Priest, Benjamin W.; Cybenko, George

    2017-05-01

    The identification of important nodes is a ubiquitous problem in the analysis of social networks. Centrality indices (such as degree centrality, closeness centrality, betweenness centrality, PageRank, and others) are used across many domains to accomplish this task. However, the computation of such indices is expensive on large graphs. Moreover, evolving graphs are becoming increasingly important in many applications. It is therefore desirable to develop on-line algorithms that can approximate centrality measures using memory sublinear in the size of the graph. We discuss the challenges facing the semi-streaming computation of many centrality indices. In particular, we apply recent advances in the streaming and sketching literature to provide a preliminary streaming approximation algorithm for degree centrality utilizing CountSketch and a multi-pass semi-streaming approximation algorithm for closeness centrality leveraging a spanner obtained through iteratively sketching the vertex-edge adjacency matrix. We also discuss possible ways forward for approximating betweenness centrality, as well as spectral measures of centrality. We provide a preliminary result using sketched low-rank approximations to approximate the output of the HITS algorithm.

  15. Quantum centrality testing on directed graphs via P T -symmetric quantum walks

    Science.gov (United States)

    Izaac, J. A.; Wang, J. B.; Abbott, P. C.; Ma, X. S.

    2017-09-01

    Various quantum-walk-based algorithms have been proposed to analyze and rank the centrality of graph vertices. However, issues arise when working with directed graphs: the resulting non-Hermitian Hamiltonian leads to nonunitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using P T -symmetric quantum walks, allowing probability-conserving nonunitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the continuous-time quantum walk provide an eigenvectorlike quantum centrality; using the P T -symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example, by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.

  16. Graph Design via Convex Optimization: Online and Distributed Perspectives

    Science.gov (United States)

    Meng, De

    Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation

  17. Interaction graphs

    DEFF Research Database (Denmark)

    Seiller, Thomas

    2016-01-01

    Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...

  18. Cyber Graph Queries for Geographically Distributed Data Centers

    Energy Technology Data Exchange (ETDEWEB)

    Berry, Jonathan W. [Mail Stop, Albuquerque, NM (United States); Collins, Michael [Christopher Newport Univ., VA (United States); Kearns, Aaron [Univ. of New Mexico, Albuquerque, NM (United States); Phillips, Cynthia A. [Mail Stop, Albuquerque, NM (United States); Saia, Jared [Univ. of New Mexico, Albuquerque, NM (United States)

    2015-05-01

    We present new algorithms for a distributed model for graph computations motivated by limited information sharing we first discussed in [20]. Two or more independent entities have collected large social graphs. They wish to compute the result of running graph algorithms on the entire set of relationships. Because the information is sensitive or economically valuable, they do not wish to simply combine the information in a single location. We consider two models for computing the solution to graph algorithms in this setting: 1) limited-sharing: the two entities can share only a polylogarithmic size subgraph; 2) low-trust: the entities must not reveal any information beyond the query answer, assuming they are all honest but curious. We believe this model captures realistic constraints on cooperating autonomous data centers. We have algorithms in both setting for s - t connectivity in both models. We also give an algorithm in the low-communication model for finding a planted clique. This is an anomaly- detection problem, finding a subgraph that is larger and denser than expected. For both the low- communication algorithms, we exploit structural properties of social networks to prove perfor- mance bounds better than what is possible for general graphs. For s - t connectivity, we use known properties. For planted clique, we propose a new property: bounded number of triangles per node. This property is based upon evidence from the social science literature. We found that classic examples of social networks do not have the bounded-triangles property. This is because many social networks contain elements that are non-human, such as accounts for a business, or other automated accounts. We describe some initial attempts to distinguish human nodes from automated nodes in social networks based only on topological properties.

  19. High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs

    Science.gov (United States)

    Kempton, Mark

    This thesis has two primary areas of focus. First we study connection graphs, which are weighted graphs in which each edge is associated with a d-dimensional rotation matrix for some fixed dimension d, in addition to a scalar weight. Second, we study non-backtracking random walks on graphs, which are random walks with the additional constraint that they cannot return to the immediately previous state at any given step. Our work in connection graphs is centered on the notion of consistency, that is, the product of rotations moving from one vertex to another is independent of the path taken, and a generalization called epsilon-consistency. We present higher dimensional versions of the combinatorial Laplacian matrix and normalized Laplacian matrix from spectral graph theory, and give results characterizing the consistency of a connection graph in terms of the spectra of these matrices. We generalize several tools from classical spectral graph theory, such as PageRank and effective resistance, to apply to connection graphs. We use these tools to give algorithms for sparsification, clustering, and noise reduction on connection graphs. In non-backtracking random walks, we address the question raised by Alon et. al. concerning how the mixing rate of a non-backtracking random walk to its stationary distribution compares to the mixing rate for an ordinary random walk. Alon et. al. address this question for regular graphs. We take a different approach, and use a generalization of Ihara's Theorem to give a new proof of Alon's result for regular graphs, and to extend the result to biregular graphs. Finally, we give a non-backtracking version of Polya's Random Walk Theorem for 2-dimensional grids.

  20. Modeling flow and transport in fracture networks using graphs

    Science.gov (United States)

    Karra, S.; O'Malley, D.; Hyman, J. D.; Viswanathan, H. S.; Srinivasan, G.

    2018-03-01

    Fractures form the main pathways for flow in the subsurface within low-permeability rock. For this reason, accurately predicting flow and transport in fractured systems is vital for improving the performance of subsurface applications. Fracture sizes in these systems can range from millimeters to kilometers. Although modeling flow and transport using the discrete fracture network (DFN) approach is known to be more accurate due to incorporation of the detailed fracture network structure over continuum-based methods, capturing the flow and transport in such a wide range of scales is still computationally intractable. Furthermore, if one has to quantify uncertainty, hundreds of realizations of these DFN models have to be run. To reduce the computational burden, we solve flow and transport on a graph representation of a DFN. We study the accuracy of the graph approach by comparing breakthrough times and tracer particle statistical data between the graph-based and the high-fidelity DFN approaches, for fracture networks with varying number of fractures and degree of heterogeneity. Due to our recent developments in capabilities to perform DFN high-fidelity simulations on fracture networks with large number of fractures, we are in a unique position to perform such a comparison. We show that the graph approach shows a consistent bias with up to an order of magnitude slower breakthrough when compared to the DFN approach. We show that this is due to graph algorithm's underprediction of the pressure gradients across intersections on a given fracture, leading to slower tracer particle speeds between intersections and longer travel times. We present a bias correction methodology to the graph algorithm that reduces the discrepancy between the DFN and graph predictions. We show that with this bias correction, the graph algorithm predictions significantly improve and the results are very accurate. The good accuracy and the low computational cost, with O (104) times lower times than

  1. Greedy Local Search and Vertex Cover in Sparse Random Graphs

    DEFF Research Database (Denmark)

    Witt, Carsten

    2009-01-01

    . This work starts with a rigorous explanation for this claim based on the refined analysis of the Karp-Sipser algorithm by Aronson et al. Subsequently, theoretical supplements are given to experimental studies of search heuristics on random graphs. For c 1, a greedy and randomized local-search heuristic...... finds an optimal cover in polynomial time with a probability arbitrarily close to 1. This behavior relies on the absence of a giant component. As an additional insight into the randomized search, it is shown that the heuristic fails badly also on graphs consisting of a single tree component of maximum......Recently, various randomized search heuristics have been studied for the solution of the minimum vertex cover problem, in particular for sparse random instances according to the G(n, c/n) model, where c > 0 is a constant. Methods from statistical physics suggest that the problem is easy if c

  2. Graph theory and its applications

    CERN Document Server

    Gross, Jonathan L

    2006-01-01

    Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

  3. Bell inequalities for graph states

    International Nuclear Information System (INIS)

    Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.

    2005-01-01

    Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)

  4. Efficient Extraction of High Centrality Vertices in Distributed Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Kumbhare, Alok [Univ. of Southern California, Los Angeles, CA (United States); Frincu, Marc [Univ. of Southern California, Los Angeles, CA (United States); Raghavendra, Cauligi S. [Univ. of Southern California, Los Angeles, CA (United States); Prasanna, Viktor K. [Univ. of Southern California, Los Angeles, CA (United States)

    2014-09-09

    Betweenness centrality (BC) is an important measure for identifying high value or critical vertices in graphs, in variety of domains such as communication networks, road networks, and social graphs. However, calculating betweenness values is prohibitively expensive and, more often, domain experts are interested only in the vertices with the highest centrality values. In this paper, we first propose a partition-centric algorithm (MS-BC) to calculate BC for a large distributed graph that optimizes resource utilization and improves overall performance. Further, we extend the notion of approximate BC by pruning the graph and removing a subset of edges and vertices that contribute the least to the betweenness values of other vertices (MSL-BC), which further improves the runtime performance. We evaluate the proposed algorithms using a mix of real-world and synthetic graphs on an HPC cluster and analyze its strengths and weaknesses. The experimental results show an improvement in performance of upto 12x for large sparse graphs as compared to the state-of-the-art, and at the same time highlights the need for better partitioning methods to enable a balanced workload across partitions for unbalanced graphs such as small-world or power-law graphs.

  5. Graph run-length matrices for histopathological image segmentation.

    Science.gov (United States)

    Tosun, Akif Burak; Gunduz-Demir, Cigdem

    2011-03-01

    The histopathological examination of tissue specimens is essential for cancer diagnosis and grading. However, this examination is subject to a considerable amount of observer variability as it mainly relies on visual interpretation of pathologists. To alleviate this problem, it is very important to develop computational quantitative tools, for which image segmentation constitutes the core step. In this paper, we introduce an effective and robust algorithm for the segmentation of histopathological tissue images. This algorithm incorporates the background knowledge of the tissue organization into segmentation. For this purpose, it quantifies spatial relations of cytological tissue components by constructing a graph and uses this graph to define new texture features for image segmentation. This new texture definition makes use of the idea of gray-level run-length matrices. However, it considers the runs of cytological components on a graph to form a matrix, instead of considering the runs of pixel intensities. Working with colon tissue images, our experiments demonstrate that the texture features extracted from "graph run-length matrices" lead to high segmentation accuracies, also providing a reasonable number of segmented regions. Compared with four other segmentation algorithms, the results show that the proposed algorithm is more effective in histopathological image segmentation.

  6. Community detection by graph Voronoi diagrams

    Science.gov (United States)

    Deritei, Dávid; Lázár, Zsolt I.; Papp, István; Járai-Szabó, Ferenc; Sumi, Róbert; Varga, Levente; Ravasz Regan, Erzsébet; Ercsey-Ravasz, Mária

    2014-06-01

    Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra- or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid- and density-based clustering methods.

  7. Distributed-Memory Breadth-First Search on Massive Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Beamer, Scott [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Madduri, Kamesh [Pennsylvania State Univ., University Park, PA (United States). Computer Science & Engineering Dept.; Asanovic, Krste [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Patterson, David [Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences

    2017-09-26

    This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.

  8. Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis

    KAUST Repository

    Kuźnik, Krzysztof

    2012-06-02

    This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.

  9. Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

    Energy Technology Data Exchange (ETDEWEB)

    Shi, Xuanhua; Luo, Xuan; Liang, Junling; Zhao, Peng; Di, Sheng; He, Bingsheng; Jin, Hai

    2018-01-01

    GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weight asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. We conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and

  10. Summary: beyond fault trees to fault graphs

    International Nuclear Information System (INIS)

    Alesso, H.P.; Prassinos, P.; Smith, C.F.

    1984-09-01

    Fault Graphs are the natural evolutionary step over a traditional fault-tree model. A Fault Graph is a failure-oriented directed graph with logic connectives that allows cycles. We intentionally construct the Fault Graph to trace the piping and instrumentation drawing (P and ID) of the system, but with logical AND and OR conditions added. Then we evaluate the Fault Graph with computer codes based on graph-theoretic methods. Fault Graph computer codes are based on graph concepts, such as path set (a set of nodes traveled on a path from one node to another) and reachability (the complete set of all possible paths between any two nodes). These codes are used to find the cut-sets (any minimal set of component failures that will fail the system) and to evaluate the system reliability

  11. A Class of Manifold Regularized Multiplicative Update Algorithms for Image Clustering.

    Science.gov (United States)

    Yang, Shangming; Yi, Zhang; He, Xiaofei; Li, Xuelong

    2015-12-01

    Multiplicative update algorithms are important tools for information retrieval, image processing, and pattern recognition. However, when the graph regularization is added to the cost function, different classes of sample data may be mapped to the same subspace, which leads to the increase of data clustering error rate. In this paper, an improved nonnegative matrix factorization (NMF) cost function is introduced. Based on the cost function, a class of novel graph regularized NMF algorithms is developed, which results in a class of extended multiplicative update algorithms with manifold structure regularization. Analysis shows that in the learning, the proposed algorithms can efficiently minimize the rank of the data representation matrix. Theoretical results presented in this paper are confirmed by simulations. For different initializations and data sets, variation curves of cost functions and decomposition data are presented to show the convergence features of the proposed update rules. Basis images, reconstructed images, and clustering results are utilized to present the efficiency of the new algorithms. Last, the clustering accuracies of different algorithms are also investigated, which shows that the proposed algorithms can achieve state-of-the-art performance in applications of image clustering.

  12. Phase-modified CTQW unable to distinguish strongly regular graphs efficiently

    International Nuclear Information System (INIS)

    Mahasinghe, A; Wijerathna, J K; Izaac, J A; Wang, J B

    2015-01-01

    Various quantum walk-based algorithms have been developed, aiming to distinguish non-isomorphic graphs with polynomial scaling, within both the discrete-time quantum walk (DTQW) and continuous-time quantum walk (CTQW) frameworks. Whilst both the single-particle DTQW and CTQW have failed to distinguish non-isomorphic strongly regular graph families (prompting the move to multi-particle graph isomorphism (GI) algorithms), the single-particle DTQW has been successfully modified by the introduction of a phase factor to distinguish a wide range of graphs in polynomial time. In this paper, we prove that an analogous phase modification to the single particle CTQW does not have the same distinguishing power as its discrete-time counterpart, in particular it cannot distinguish strongly regular graphs with the same family parameters with the same efficiency. (paper)

  13. Augmented marked graphs

    CERN Document Server

    Cheung, King Sing

    2014-01-01

    Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume

  14. Use of graph algorithms in the processing and analysis of images with focus on the biomedical data.

    Science.gov (United States)

    Zdimalova, M; Roznovjak, R; Weismann, P; El Falougy, H; Kubikova, E

    2017-01-01

    Image segmentation is a known problem in the field of image processing. A great number of methods based on different approaches to this issue was created. One of these approaches utilizes the findings of the graph theory. Our work focuses on segmentation using shortest paths in a graph. Specifically, we deal with methods of "Intelligent Scissors," which use Dijkstra's algorithm to find the shortest paths. We created a new software in Microsoft Visual Studio 2013 integrated development environment Visual C++ in the language C++/CLI. We created a format application with a graphical users development environment for system Windows, with using the platform .Net (version 4.5). The program was used for handling and processing the original medical data. The major disadvantage of the method of "Intelligent Scissors" is the computational time length of Dijkstra's algorithm. However, after the implementation of a more efficient priority queue, this problem could be alleviated. The main advantage of this method we see in training that enables to adapt to a particular kind of edge, which we need to segment. The user involvement has a significant influence on the process of segmentation, which enormously aids to achieve high-quality results (Fig. 7, Ref. 13).

  15. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  16. Towards a theory of geometric graphs

    CERN Document Server

    Pach, Janos

    2004-01-01

    The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

  17. Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

    OpenAIRE

    Chen, Pin-Yu; Hero, Alfred O.

    2017-01-01

    Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal plus noise model, we provide a phase transition analys...

  18. Mizan: Optimizing Graph Mining in Large Parallel Systems

    KAUST Repository

    Kalnis, Panos

    2012-03-01

    Extracting information from graphs, from nding shortest paths to complex graph mining, is essential for many ap- plications. Due to the shear size of modern graphs (e.g., social networks), processing must be done on large paral- lel computing infrastructures (e.g., the cloud). Earlier ap- proaches relied on the MapReduce framework, which was proved inadequate for graph algorithms. More recently, the message passing model (e.g., Pregel) has emerged. Although the Pregel model has many advantages, it is agnostic to the graph properties and the architecture of the underlying com- puting infrastructure, leading to suboptimal performance. In this paper, we propose Mizan, a layer between the users\\' code and the computing infrastructure. Mizan considers the structure of the input graph and the architecture of the in- frastructure in order to: (i) decide whether it is bene cial to generate a near-optimal partitioning of the graph in a pre- processing step, and (ii) choose between typical point-to- point message passing and a novel approach that puts com- puting nodes in a virtual overlay ring. We deployed Mizan on a small local Linux cluster, on the cloud (256 virtual machines in Amazon EC2), and on an IBM Blue Gene/P supercomputer (1024 CPUs). We show that Mizan executes common algorithms on very large graphs 1-2 orders of mag- nitude faster than MapReduce-based implementations and up to one order of magnitude faster than implementations relying on Pregel-like hash-based graph partitioning.

  19. Graph-based unsupervised segmentation algorithm for cultured neuronal networks' structure characterization and modeling.

    Science.gov (United States)

    de Santos-Sierra, Daniel; Sendiña-Nadal, Irene; Leyva, Inmaculada; Almendral, Juan A; Ayali, Amir; Anava, Sarit; Sánchez-Ávila, Carmen; Boccaletti, Stefano

    2015-06-01

    Large scale phase-contrast images taken at high resolution through the life of a cultured neuronal network are analyzed by a graph-based unsupervised segmentation algorithm with a very low computational cost, scaling linearly with the image size. The processing automatically retrieves the whole network structure, an object whose mathematical representation is a matrix in which nodes are identified neurons or neurons' clusters, and links are the reconstructed connections between them. The algorithm is also able to extract any other relevant morphological information characterizing neurons and neurites. More importantly, and at variance with other segmentation methods that require fluorescence imaging from immunocytochemistry techniques, our non invasive measures entitle us to perform a longitudinal analysis during the maturation of a single culture. Such an analysis furnishes the way of individuating the main physical processes underlying the self-organization of the neurons' ensemble into a complex network, and drives the formulation of a phenomenological model yet able to describe qualitatively the overall scenario observed during the culture growth. © 2014 International Society for Advancement of Cytometry.

  20. On the centrality of some graphs

    Directory of Open Access Journals (Sweden)

    Vecdi Aytac

    2017-10-01

    Full Text Available A central issue in the analysis of complex networks is the assessment of their stability and vulnerability. A variety of measures have been proposed in the literature to quantify the stability of networks and a number of graph-theoretic parameters have been used to derive formulas for calculating network reliability. Different measures for graph vulnerability have been introduced so far to study different aspects of the graph behavior after removal of vertices or links such as connectivity, toughness, scattering number, binding number, residual closeness and integrity. In this paper, we consider betweenness centrality of a graph. Betweenness centrality of a vertex of a graph is portion of the shortest paths all pairs of vertices passing through a given vertex. In this paper, we obtain exact values for betweenness centrality for some wheel related graphs namely gear, helm, sunflower and friendship graphs.

  1. Efficient graph algorithms

    Indian Academy of Sciences (India)

    Shortest path problems. Road network on cities and we want to navigate between cities. . – p.8/30 ..... The rest of the talk... Computing connectivities between all pairs of vertices good algorithm wrt both space and time to compute the exact solution. . – p.15/30 ...

  2. Simulating activation propagation in social networks using the graph theory

    Directory of Open Access Journals (Sweden)

    František Dařena

    2010-01-01

    Full Text Available The social-network formation and analysis is nowadays one of objects that are in a focus of intensive research. The objective of the paper is to suggest the perspective of representing social networks as graphs, with the application of the graph theory to problems connected with studying the network-like structures and to study spreading activation algorithm for reasons of analyzing these structures. The paper presents the process of modeling multidimensional networks by means of directed graphs with several characteristics. The paper also demonstrates using Spreading Activation algorithm as a good method for analyzing multidimensional network with the main focus on recommender systems. The experiments showed that the choice of parameters of the algorithm is crucial, that some kind of constraint should be included and that the algorithm is able to provide a stable environment for simulations with networks.

  3. Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

    Science.gov (United States)

    Shang, Yilun

    2015-01-01

    Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

  4. Graph Sampling for Covariance Estimation

    KAUST Repository

    Chepuri, Sundeep Prabhakar

    2017-04-25

    In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.

  5. Cardinality Estimation Algorithm in Large-Scale Anonymous Wireless Sensor Networks

    KAUST Repository

    Douik, Ahmed

    2017-08-30

    Consider a large-scale anonymous wireless sensor network with unknown cardinality. In such graphs, each node has no information about the network topology and only possesses a unique identifier. This paper introduces a novel distributed algorithm for cardinality estimation and topology discovery, i.e., estimating the number of node and structure of the graph, by querying a small number of nodes and performing statistical inference methods. While the cardinality estimation allows the design of more efficient coding schemes for the network, the topology discovery provides a reliable way for routing packets. The proposed algorithm is shown to produce a cardinality estimate proportional to the best linear unbiased estimator for dense graphs and specific running times. Simulation results attest the theoretical results and reveal that, for a reasonable running time, querying a small group of nodes is sufficient to perform an estimation of 95% of the whole network. Applications of this work include estimating the number of Internet of Things (IoT) sensor devices, online social users, active protein cells, etc.

  6. Replica methods for loopy sparse random graphs

    International Nuclear Information System (INIS)

    Coolen, ACC

    2016-01-01

    I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)

  7. MATHEMATICA APPLICATION FOR GRAPH COLORING AT THE INTERSECTION OF JALAN PANGERAN ANTASARI JAKARTA

    Directory of Open Access Journals (Sweden)

    Suwarno Suwarno

    2017-12-01

    Full Text Available This research examines about graph coloring using Welch-Powell algorithm. This research begins by trying to understand about graph coloring and its algorithm. The case study was conducted at the intersection of Pangeran Antasari Street. In the formation of graph obtained 12 vertices as traffic flow and 16 edges as traffic path. The results of this study obtained 4 chromatic numbers which describes 4 stages of traffic light arrangement. This paper also explains the application of Mathematica software in graph coloring.

  8. Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.

    Directory of Open Access Journals (Sweden)

    Yilun Shang

    Full Text Available Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

  9. Upper-Lower Bounds Candidate Sets Searching Algorithm for Bayesian Network Structure Learning

    Directory of Open Access Journals (Sweden)

    Guangyi Liu

    2014-01-01

    Full Text Available Bayesian network is an important theoretical model in artificial intelligence field and also a powerful tool for processing uncertainty issues. Considering the slow convergence speed of current Bayesian network structure learning algorithms, a fast hybrid learning method is proposed in this paper. We start with further analysis of information provided by low-order conditional independence testing, and then two methods are given for constructing graph model of network, which is theoretically proved to be upper and lower bounds of the structure space of target network, so that candidate sets are given as a result; after that a search and scoring algorithm is operated based on the candidate sets to find the final structure of the network. Simulation results show that the algorithm proposed in this paper is more efficient than similar algorithms with the same learning precision.

  10. Bipartite separability and nonlocal quantum operations on graphs

    Science.gov (United States)

    Dutta, Supriyo; Adhikari, Bibhas; Banerjee, Subhashish; Srikanth, R.

    2016-07-01

    In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for separability, although there are entangled states with positive partial transpose for which the degree criterion fails. Here we introduce the concept of partially symmetric graphs and degree symmetric graphs by using the well-known concept of partial transposition of a graph and degree criteria, respectively. Thus, we provide classes of bipartite separable states of dimension m ×n arising from partially symmetric graphs. We identify partially asymmetric graphs that lack the property of partial symmetry. We develop a combinatorial procedure to create a partially asymmetric graph from a given partially symmetric graph. We show that this combinatorial operation can act as an entanglement generator for mixed states arising from partially symmetric graphs.

  11. Graph theory and the Virasoro master equation

    International Nuclear Information System (INIS)

    Obers, N.A.J.

    1991-01-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) metric in the Pauli-like basis of SU(n). Finally, he defines the 'sine-area graphs' of SU(n), which label the conformal field theories of SU(n) metric , and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g metric

  12. Graph reconstruction with a betweenness oracle

    DEFF Research Database (Denmark)

    Abrahamsen, Mikkel; Bodwin, Greg; Rotenberg, Eva

    2016-01-01

    Graph reconstruction algorithms seek to learn a hidden graph by repeatedly querying a blackbox oracle for information about the graph structure. Perhaps the most well studied and applied version of the problem uses a distance oracle, which can report the shortest path distance between any pair...... of nodes. We introduce and study the betweenness oracle, where bet(a, m, z) is true iff m lies on a shortest path between a and z. This oracle is strictly weaker than a distance oracle, in the sense that a betweenness query can be simulated by a constant number of distance queries, but not vice versa...

  13. Network reconstruction via graph blending

    Science.gov (United States)

    Estrada, Rolando

    2016-05-01

    Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.

  14. Many-core graph analytics using accelerated sparse linear algebra routines

    Science.gov (United States)

    Kozacik, Stephen; Paolini, Aaron L.; Fox, Paul; Kelmelis, Eric

    2016-05-01

    Graph analytics is a key component in identifying emerging trends and threats in many real-world applications. Largescale graph analytics frameworks provide a convenient and highly-scalable platform for developing algorithms to analyze large datasets. Although conceptually scalable, these techniques exhibit poor performance on modern computational hardware. Another model of graph computation has emerged that promises improved performance and scalability by using abstract linear algebra operations as the basis for graph analysis as laid out by the GraphBLAS standard. By using sparse linear algebra as the basis, existing highly efficient algorithms can be adapted to perform computations on the graph. This approach, however, is often less intuitive to graph analytics experts, who are accustomed to vertex-centric APIs such as Giraph, GraphX, and Tinkerpop. We are developing an implementation of the high-level operations supported by these APIs in terms of linear algebra operations. This implementation is be backed by many-core implementations of the fundamental GraphBLAS operations required, and offers the advantages of both the intuitive programming model of a vertex-centric API and the performance of a sparse linear algebra implementation. This technology can reduce the number of nodes required, as well as the run-time for a graph analysis problem, enabling customers to perform more complex analysis with less hardware at lower cost. All of this can be accomplished without the requirement for the customer to make any changes to their analytics code, thanks to the compatibility with existing graph APIs.

  15. Determining X-chains in graph states

    International Nuclear Information System (INIS)

    Wu, Jun-Yi; Kampermann, Hermann; Bruß, Dagmar

    2016-01-01

    The representation of graph states in the X-basis as well as the calculation of graph state overlaps can efficiently be performed by using the concept of X-chains (Wu et al 2015 Phys. Rev. A 92 012322). We present a necessary and sufficient criterion for X-chains and show that they can efficiently be determined by the Bareiss algorithm. An analytical approach for searching X-chain groups of a graph state is proposed. Furthermore we generalize the concept of X-chains to so-called Euler chains, whose induced subgraphs are Eulerian. This approach helps to determine if a given vertex set is an X-chain and we show how Euler chains can be used in the construction of multipartite Bell inequalities for graph states. (paper)

  16. Degree-based graph construction

    International Nuclear Information System (INIS)

    Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A

    2009-01-01

    Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)

  17. PAGANI Toolkit: Parallel graph-theoretical analysis package for brain network big data.

    Science.gov (United States)

    Du, Haixiao; Xia, Mingrui; Zhao, Kang; Liao, Xuhong; Yang, Huazhong; Wang, Yu; He, Yong

    2018-05-01

    The recent collection of unprecedented quantities of neuroimaging data with high spatial resolution has led to brain network big data. However, a toolkit for fast and scalable computational solutions is still lacking. Here, we developed the PArallel Graph-theoretical ANalysIs (PAGANI) Toolkit based on a hybrid central processing unit-graphics processing unit (CPU-GPU) framework with a graphical user interface to facilitate the mapping and characterization of high-resolution brain networks. Specifically, the toolkit provides flexible parameters for users to customize computations of graph metrics in brain network analyses. As an empirical example, the PAGANI Toolkit was applied to individual voxel-based brain networks with ∼200,000 nodes that were derived from a resting-state fMRI dataset of 624 healthy young adults from the Human Connectome Project. Using a personal computer, this toolbox completed all computations in ∼27 h for one subject, which is markedly less than the 118 h required with a single-thread implementation. The voxel-based functional brain networks exhibited prominent small-world characteristics and densely connected hubs, which were mainly located in the medial and lateral fronto-parietal cortices. Moreover, the female group had significantly higher modularity and nodal betweenness centrality mainly in the medial/lateral fronto-parietal and occipital cortices than the male group. Significant correlations between the intelligence quotient and nodal metrics were also observed in several frontal regions. Collectively, the PAGANI Toolkit shows high computational performance and good scalability for analyzing connectome big data and provides a friendly interface without the complicated configuration of computing environments, thereby facilitating high-resolution connectomics research in health and disease. © 2018 Wiley Periodicals, Inc.

  18. Abnormalities of functional brain networks in pathological gambling: a graph-theoretical approach

    Science.gov (United States)

    Tschernegg, Melanie; Crone, Julia S.; Eigenberger, Tina; Schwartenbeck, Philipp; Fauth-Bühler, Mira; Lemènager, Tagrid; Mann, Karl; Thon, Natasha; Wurst, Friedrich M.; Kronbichler, Martin

    2013-01-01

    Functional neuroimaging studies of pathological gambling (PG) demonstrate alterations in frontal and subcortical regions of the mesolimbic reward system. However, most investigations were performed using tasks involving reward processing or executive functions. Little is known about brain network abnormalities during task-free resting state in PG. In the present study, graph-theoretical methods were used to investigate network properties of resting state functional magnetic resonance imaging data in PG. We compared 19 patients with PG to 19 healthy controls (HCs) using the Graph Analysis Toolbox (GAT). None of the examined global metrics differed between groups. At the nodal level, pathological gambler showed a reduced clustering coefficient in the left paracingulate cortex and the left juxtapositional lobe (supplementary motor area, SMA), reduced local efficiency in the left SMA, as well as an increased node betweenness for the left and right paracingulate cortex and the left SMA. At an uncorrected threshold level, the node betweenness in the left inferior frontal gyrus was decreased and increased in the caudate. Additionally, increased functional connectivity between fronto-striatal regions and within frontal regions has also been found for the gambling patients. These findings suggest that regions associated with the reward system demonstrate reduced segregation but enhanced integration while regions associated with executive functions demonstrate reduced integration. The present study makes evident that PG is also associated with abnormalities in the topological network structure of the brain during rest. Since alterations in PG cannot be explained by direct effects of abused substances on the brain, these findings will be of relevance for understanding functional connectivity in other addictive disorders. PMID:24098282

  19. Abnormalities of Functional Brain Networks in Pathological Gambling: A Graph-Theoretical Approach

    Directory of Open Access Journals (Sweden)

    Melanie eTschernegg

    2013-09-01

    Full Text Available Functional neuroimaging studies of pathological gambling demonstrate alterations in frontal and subcortical regions of the mesolimbic reward system. However, most investigations were performed using tasks involving reward processing or executive functions. Little is known about brain network abnormalities during task-free resting state in pathological gambling. In the present study, graph-theoretical methods were used to investigate network properties of resting state functional MRI data in pathological gambling. We compared 19 patients with pathological gambling to 19 healthy controls using the Graph Analysis Toolbox (GAT. None of the examined global metrics differed between groups. At the nodal level, pathological gambler showed a reduced clustering coefficient in the left paracingulate cortex and the left juxtapositional lobe (SMA, reduced local efficiency in the left SMA, as well as an increased node betweenness for the left and right paracingulate cortex and the left SMA. At an uncorrected threshold level, the node betweenness in the left inferior frontal gyrus was decreased and increased in the caudate. Additionally, increased functional connectivity between fronto-striatal regions and within frontal regions has also been found for the gambling patients.These findings suggest that regions associated with the reward system demonstrate reduced segregation but enhanced integration while regions associated with executive functions demonstrate reduced integration. The present study makes evident that pathological gambling is also associated with abnormalities in the topological network structure of the brain during rest. Since alterations in pathological gambling cannot be explained by direct effects of abused substances on the brain, these findings will be of relevance for understanding functional connectivity in other addictive disorders.

  20. Executable Pseudocode for Graph Algorithms

    NARCIS (Netherlands)

    B. Ó Nualláin (Breanndán)

    2015-01-01

    textabstract Algorithms are written in pseudocode. However the implementation of an algorithm in a conventional, imperative programming language can often be scattered over hundreds of lines of code thus obscuring its essence. This can lead to difficulties in understanding or verifying the

  1. Graph processing platforms at scale: practices and experiences

    Energy Technology Data Exchange (ETDEWEB)

    Lim, Seung-Hwan [ORNL; Lee, Sangkeun (Matt) [ORNL; Brown, Tyler C [ORNL; Sukumar, Sreenivas R [ORNL; Ganesh, Gautam [ORNL

    2015-01-01

    Graph analysis unveils hidden associations of data in many phenomena and artifacts, such as road network, social networks, genomic information, and scientific collaboration. Unfortunately, a wide diversity in the characteristics of graphs and graph operations make it challenging to find a right combination of tools and implementation of algorithms to discover desired knowledge from the target data set. This study presents an extensive empirical study of three representative graph processing platforms: Pegasus, GraphX, and Urika. Each system represents a combination of options in data model, processing paradigm, and infrastructure. We benchmarked each platform using three popular graph operations, degree distribution, connected components, and PageRank over a variety of real-world graphs. Our experiments show that each graph processing platform shows different strength, depending the type of graph operations. While Urika performs the best in non-iterative operations like degree distribution, GraphX outputforms iterative operations like connected components and PageRank. In addition, we discuss challenges to optimize the performance of each platform over large scale real world graphs.

  2. Wiener index and Diameter of a Planar Graph in Subquadratic Time

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    2009-01-01

    Consider the problem of computing the sum of distances between each pair of vertices of an unweighted graph. This sum is also known as the Wiener index of the graph, a generalization of a definition given by H. Wiener in 1947. A molecular topological index is a value obtained from the graph...... structure of a molecule such that this value (hopefully) correlates with physical and/or chemical properties of the molecule. The Wiener index is perhaps the most studied molecular topological index with more than a thousand publications. It is open whether the Wiener index of a planar graph can be obtained...... in subquadratic time. In my talk, I will solve this open problem by exhibiting an O(n2 log log n / log n) time algorithm, where n is the size of the graph. A simple modification yields an algorithm with the same time bound that computes the diameter (maximum distance between any vertex pair) of a planar graph. I...

  3. GraphStore: A Distributed Graph Storage System for Big Data Networks

    Science.gov (United States)

    Martha, VenkataSwamy

    2013-01-01

    Networks, such as social networks, are a universal solution for modeling complex problems in real time, especially in the Big Data community. While previous studies have attempted to enhance network processing algorithms, none have paved a path for the development of a persistent storage system. The proposed solution, GraphStore, provides an…

  4. A New Graph Drawing Scheme for Social Network

    Directory of Open Access Journals (Sweden)

    Eric Ke Wang

    2014-01-01

    visualization is employed to extract the potential information from the large scale of social network data and present the information briefly as visualized graphs. In the process of information visualization, graph drawing is a crucial part. In this paper, we study the graph layout algorithms and propose a new graph drawing scheme combining multilevel and single-level drawing approaches, including the graph division method based on communities and refining approach based on partitioning strategy. Besides, we compare the effectiveness of our scheme and FM3 in experiments. The experiment results show that our scheme can achieve a clearer diagram and effectively extract the community structure of the social network to be applied to drawing schemes.

  5. The Partial Mapping of the Web Graph

    Directory of Open Access Journals (Sweden)

    Kristina Machova

    2009-06-01

    Full Text Available The paper presents an approach to partial mapping of a web sub-graph. This sub-graph contains the nearest surroundings of an actual web page. Our work deals with acquiring relevant Hyperlinks of a base web site, generation of adjacency matrix, the nearest distance matrix and matrix of converted distances of Hyperlinks, detection of compactness of web representation, and visualization of its graphical representation. The paper introduces an LWP algorithm – a technique for Hyperlink filtration.  This work attempts to help users with the orientation within the web graph.

  6. Distributed Large Independent Sets in One Round On Bounded-independence Graphs

    OpenAIRE

    Halldorsson , Magnus M.; Konrad , Christian

    2015-01-01

    International audience; We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is O((log(n)/log(log(n)))^2).A starting point of our w...

  7. Polyhedral Computations for the Simple Graph Partitioning Problem

    DEFF Research Database (Denmark)

    Sørensen, Michael Malmros

    The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each containing no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we present a branch-and-cut algorithm for the problem that ...

  8. Regularities and dynamics in bisimulation reductions of big graphs

    NARCIS (Netherlands)

    Luo, Y.; Fletcher, G.H.L.; Hidders, A.J.H.; De Bra, P.M.E.; Wu, Y.

    2013-01-01

    Bisimulation is a basic graph reduction operation, which plays a key role in a wide range of graph analytical applications. While there are many algorithms dedicated to computing bisimulation results, to our knowledge, little work has been done to analyze the results themselves. Since data

  9. Algorithms for Academic Search and Recommendation Systems

    DEFF Research Database (Denmark)

    Amolochitis, Emmanouil

    2014-01-01

    are part of a developed Movie Recommendation system, the first such system to be commercially deployed in Greece by a major Triple Play services provider. In the third part of the work we present the design of a quantitative association rule mining algorithm. The introduced mining algorithm processes......In this work we present novel algorithms for academic search, recommendation and association rules mining. In the first part of the work we introduce a novel hierarchical heuristic scheme for re-ranking academic publications. The scheme is based on the hierarchical combination of a custom...... implementation of the term frequency heuristic, a time-depreciated citation score and a graph-theoretic computed score that relates the paper’s index terms with each other. On the second part we describe the design of hybrid recommender ensemble (user, item and content based). The newly introduced algorithms...

  10. Three-coloring graphs with no induced seven-vertex path II : using a triangle

    OpenAIRE

    Chudnovsky, Maria; Maceli, Peter; Zhong, Mingxian

    2015-01-01

    In this paper, we give a polynomial time algorithm which determines if a given graph containing a triangle and no induced seven-vertex path is 3-colorable, and gives an explicit coloring if one exists. In previous work, we gave a polynomial time algorithm for three-coloring triangle-free graphs with no induced seven-vertex path. Combined, our work shows that three-coloring a graph with no induced seven-vertex path can be done in polynomial time.

  11. Hierarchy of modular graph identities

    Energy Technology Data Exchange (ETDEWEB)

    D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)

    2016-11-09

    The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

  12. Hierarchy of modular graph identities

    International Nuclear Information System (INIS)

    D’Hoker, Eric; Kaidi, Justin

    2016-01-01

    The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.

  13. Joint Graph Layouts for Visualizing Collections of Segmented Meshes

    KAUST Repository

    Ren, Jing

    2017-09-12

    We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

  14. Joint Graph Layouts for Visualizing Collections of Segmented Meshes

    KAUST Repository

    Ren, Jing; Schneider, Jens; Ovsjanikov, Maks; Wonka, Peter

    2017-01-01

    We present a novel and efficient approach for computing joint graph layouts and then use it to visualize collections of segmented meshes. Our joint graph layout algorithm takes as input the adjacency matrices for a set of graphs along with partial, possibly soft, correspondences between nodes of different graphs. We then use a two stage procedure, where in the first step, we extend spectral graph drawing to include a consistency term so that a collection of graphs can be handled jointly. Our second step extends metric multi-dimensional scaling with stress majorization to the joint layout setting, while using the output of the spectral approach as initialization. Further, we discuss a user interface for exploring a collection of graphs. Finally, we show multiple example visualizations of graphs stemming from collections of segmented meshes and we present qualitative and quantitative comparisons with previous work.

  15. Research of Subgraph Estimation Page Rank Algorithm for Web Page Rank

    Directory of Open Access Journals (Sweden)

    LI Lan-yin

    2017-04-01

    Full Text Available The traditional PageRank algorithm can not efficiently perform large data Webpage scheduling problem. This paper proposes an accelerated algorithm named topK-Rank,which is based on PageRank on the MapReduce platform. It can find top k nodes efficiently for a given graph without sacrificing accuracy. In order to identify top k nodes,topK-Rank algorithm prunes unnecessary nodes and edges in each iteration to dynamically construct subgraphs,and iteratively estimates lower/upper bounds of PageRank scores through subgraphs. Theoretical analysis shows that this method guarantees result exactness. Experiments show that topK-Rank algorithm can find k nodes much faster than the existing approaches.

  16. Predicting conversion from MCI to AD using resting-state fMRI, graph theoretical approach and SVM.

    Science.gov (United States)

    Hojjati, Seyed Hani; Ebrahimzadeh, Ata; Khazaee, Ali; Babajani-Feremi, Abbas

    2017-04-15

    We investigated identifying patients with mild cognitive impairment (MCI) who progress to Alzheimer's disease (AD), MCI converter (MCI-C), from those with MCI who do not progress to AD, MCI non-converter (MCI-NC), based on resting-state fMRI (rs-fMRI). Graph theory and machine learning approach were utilized to predict progress of patients with MCI to AD using rs-fMRI. Eighteen MCI converts (average age 73.6 years; 11 male) and 62 age-matched MCI non-converters (average age 73.0 years, 28 male) were included in this study. We trained and tested a support vector machine (SVM) to classify MCI-C from MCI-NC using features constructed based on the local and global graph measures. A novel feature selection algorithm was developed and utilized to select an optimal subset of features. Using subset of optimal features in SVM, we classified MCI-C from MCI-NC with an accuracy, sensitivity, specificity, and the area under the receiver operating characteristic (ROC) curve of 91.4%, 83.24%, 90.1%, and 0.95, respectively. Furthermore, results of our statistical analyses were used to identify the affected brain regions in AD. To the best of our knowledge, this is the first study that combines the graph measures (constructed based on rs-fMRI) with machine learning approach and accurately classify MCI-C from MCI-NC. Results of this study demonstrate potential of the proposed approach for early AD diagnosis and demonstrate capability of rs-fMRI to predict conversion from MCI to AD by identifying affected brain regions underlying this conversion. Copyright © 2017 Elsevier B.V. All rights reserved.

  17. Commuting graphs of matrix algebras

    International Nuclear Information System (INIS)

    Akbari, S.; Bidkhori, H.; Mohammadian, A.

    2006-08-01

    The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)

  18. Generating Realistic Labelled, Weighted Random Graphs

    Directory of Open Access Journals (Sweden)

    Michael Charles Davis

    2015-12-01

    Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

  19. On The Roman Domination Stable Graphs

    Directory of Open Access Journals (Sweden)

    Hajian Majid

    2017-11-01

    Full Text Available A Roman dominating function (or just RDF on a graph G = (V,E is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u = 0 is adjacent to at least one vertex v for which f(v = 2. The weight of an RDF f is the value f(V (G = Pu2V (G f(u. The Roman domination number of a graph G, denoted by R(G, is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016 1650049].

  20. POOR TEXTURAL IMAGE MATCHING BASED ON GRAPH THEORY

    Directory of Open Access Journals (Sweden)

    S. Chen

    2016-06-01

    Full Text Available Image matching lies at the heart of photogrammetry and computer vision. For poor textural images, the matching result is affected by low contrast, repetitive patterns, discontinuity or occlusion, few or homogeneous textures. Recently, graph matching became popular for its integration of geometric and radiometric information. Focused on poor textural image matching problem, it is proposed an edge-weight strategy to improve graph matching algorithm. A series of experiments have been conducted including 4 typical landscapes: Forest, desert, farmland, and urban areas. And it is experimentally found that our new algorithm achieves better performance. Compared to SIFT, doubled corresponding points were acquired, and the overall recall rate reached up to 68%, which verifies the feasibility and effectiveness of the algorithm.

  1. Top-k Keyword Search Over Graphs Based On Backward Search

    Directory of Open Access Journals (Sweden)

    Zeng Jia-Hui

    2017-01-01

    Full Text Available Keyword search is one of the most friendly and intuitive information retrieval methods. Using the keyword search to get the connected subgraph has a lot of application in the graph-based cognitive computation, and it is a basic technology. This paper focuses on the top-k keyword searching over graphs. We implemented a keyword search algorithm which applies the backward search idea. The algorithm locates the keyword vertices firstly, and then applies backward search to find rooted trees that contain query keywords. The experiment shows that query time is affected by the iteration number of the algorithm.

  2. Parameterized Algorithms for Survivable Network Design with Uniform Demands

    DEFF Research Database (Denmark)

    Bang-Jensen, Jørgen; Klinkby Knudsen, Kristine Vitting; Saurabh, Saket

    2018-01-01

    problem in combinatorial optimization that captures numerous well-studied problems in graph theory and graph algorithms. Consequently, there is a long line of research into exact-polynomial time algorithms as well as approximation algorithms for various restrictions of this problem. An important...... that SNDP is W[1]-hard for both arc and vertex connectivity versions on digraphs. The core of our algorithms is composed of new combinatorial results on connectivity in digraphs and undirected graphs....

  3. Expander graphs in pure and applied mathematics

    OpenAIRE

    Lubotzky, Alexander

    2012-01-01

    Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number theory, group theory, geometry and more. This expository article describes their constructions and various applications in pure and applied mathematics.

  4. A scalable community detection algorithm for large graphs using stochastic block models

    KAUST Repository

    Peng, Chengbin

    2017-11-24

    Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of

  5. A scalable community detection algorithm for large graphs using stochastic block models

    KAUST Repository

    Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.

    2017-01-01

    Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of

  6. Handbook of graph drawing and visualization

    CERN Document Server

    Tamassia, Roberto

    2013-01-01

    Planarity Testing and Embedding Maurizio PatrignaniCrossings and Planarization Christoph Buchheim, Markus Chimani, Carsten Gutwenger, Michael Jünger, and Petra MutzelSymmetric Graph Drawing Peter Eades and Seok-Hee HongProximity Drawings Giuseppe LiottaTree Drawing Algorithms Adrian RusuPlanar Straight-Line Drawing Algorithms Luca VismaraPlanar Orthogonal and Polyline Drawing Algorithms Christian A. Duncan and Michael T. GoodrichSpine and Radial Drawings Emilio Di Giacomo, Walter Didimo, and Giuseppe LiottaCircular Drawing Algorithms Janet M. Six and Ioannis G. TollisRectangular Drawing Algori

  7. Using graph theory for automated electric circuit solving

    International Nuclear Information System (INIS)

    Toscano, L; Stella, S; Milotti, E

    2015-01-01

    Graph theory plays many important roles in modern physics and in many different contexts, spanning diverse topics such as the description of scale-free networks and the structure of the universe as a complex directed graph in causal set theory. Graph theory is also ideally suited to describe many concepts in computer science. Therefore it is increasingly important for physics students to master the basic concepts of graph theory. Here we describe a student project where we develop a computational approach to electric circuit solving which is based on graph theoretic concepts. This highly multidisciplinary approach combines abstract mathematics, linear algebra, the physics of circuits, and computer programming to reach the ambitious goal of implementing automated circuit solving. (paper)

  8. Box graphs and resolutions I

    Directory of Open Access Journals (Sweden)

    Andreas P. Braun

    2016-04-01

    Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.

  9. Proceedings 3rd Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014)

    DEFF Research Database (Denmark)

    2014-01-01

    is to foster the convergence on research interests from several communities dealing with graph analysis in all its forms in computer science, with a particular attention to software development and analysis. Graphs are used to represent data and processes in many application areas, and they are subjected......These are the proceedings of the Third Workshop on GRAPH Inspection and Traversal Engineering (GRAPHITE 2014), which took place on April 5, 2014 in Grenoble, France, as a satellite event of the 17th European Joint Conferences on Theory and Practice of Software (ETAPS 2014). The aim of GRAPHITE...... to various computational algorithms in order to analyze them. Just restricting the attention to the analysis of software, graph analysis algorithms are used, for instance, to verify properties using model checking techniques that explore the system's state space graph or static analysis techniques based...

  10. Chromatic polynomials of random graphs

    International Nuclear Information System (INIS)

    Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian

    2010-01-01

    Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

  11. Parallel assembling and equation solving via graph algorithms with an application to the FE simulation of metal extrusion processes

    CERN Document Server

    Unterkircher, A

    2005-01-01

    We propose methods for parallel assembling and iterative equation solving based on graph algorithms. The assembling technique is independent of dimension, element type and model shape. As a parallel solving technique we construct a multiplicative symmetric Schwarz preconditioner for the conjugate gradient method. Both methods have been incorporated into a non-linear FE code to simulate 3D metal extrusion processes. We illustrate the efficiency of these methods on shared memory computers by realistic examples.

  12. Modular Environment for Graph Research and Analysis with a Persistent

    Energy Technology Data Exchange (ETDEWEB)

    2009-11-18

    The MEGRAPHS software package provides a front-end to graphs and vectors residing on special-purpose computing resources. It allows these data objects to be instantiated, destroyed, and manipulated. A variety of primitives needed for typical graph analyses are provided. An example program illustrating how MEGRAPHS can be used to implement a PageRank computation is included in the distribution.The MEGRAPHS software package is targeted towards developers of graph algorithms. Programmers using MEGRAPHS would write graph analysis programs in terms of high-level graph and vector operations. These computations are transparently executed on the Cray XMT compute nodes.

  13. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory

    Science.gov (United States)

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A.

    2016-01-01

    There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of “maximum flow-minimum cut” graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered. PMID:27089174

  14. Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.

    Science.gov (United States)

    Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A

    2016-08-25

    There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.

  15. Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.

    Science.gov (United States)

    Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing

    2018-03-01

    In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.

  16. Social Graph Community Differentiated by Node Features with Partly Missing Information

    Directory of Open Access Journals (Sweden)

    V. O. Chesnokov

    2015-01-01

    Full Text Available This paper proposes a new algorithm for community differentiation in social graphs, which uses information both on the graph structure and on the vertices. We consider user's ego-network i.e. his friends, with no himself, where each vertex has a set of features such as details on a workplace, institution, etc. The task is to determine missing or unspecified features of the vertices, based on their neighbors' features, and use these features to differentiate the communities in the social graph. Two vertices are believed to belong to the same community if they have a common feature. A hypothesis has been put forward that if most neighbors of a vertex have a common feature, there is a good probability that the vertex has this feature as well. The proposed algorithm is iterative and updates features of vertices, based on its neighbors, according to the hypothesis. Share of neighbors that form a majority is specified by the algorithm parameter. Complexity of single iteration depends linearly on the number of edges in the graph.To assess the quality of clustering three normalized metrics were used, namely: expected density, silhouette index, and Hubert's Gamma Statistic. The paper describes a method for test sampling of 2.000 graphs of the user's social network \\VKontakte". The API requests addressed \\VKontakte" and parsing HTML-pages of user's profiles and search results provided crawling. Information on user's group membership, secondary and higher education, and workplace was used as features. To store data the PostgreSQL DBMS was used, and the gexf format was used for data processing. For the test sample, metrics for several values of algorithm parameter were estimated: the value of index silhouettes was low (0.14-0.20, but within the normal range; the value of expected density was high, i.e. 1.17-1.52; the value of Hubert's gamma statistic was 0.94-0.95 that is close to the maximum. The number of vertices with no features was calculated before

  17. Hierarchical graphs for rule-based modeling of biochemical systems

    Directory of Open Access Journals (Sweden)

    Hu Bin

    2011-02-01

    Full Text Available Abstract Background In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal of an edge represents a class of association (dissociation reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system. Results For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm. Conclusions Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for

  18. Note on Ideal Based Zero-Divisor Graph of a Commutative Ring

    Directory of Open Access Journals (Sweden)

    Mallika A.

    2017-12-01

    Full Text Available In this paper, we consider the ideal based zero divisor graph ΓI(R of a commutative ring R. We discuss some graph theoretical properties of ΓI(R in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI(R with that of Γ(R/I . Further we determine a necessary and sufficient condition for the graph to be Eulerian and regular.

  19. Digital Geometry Algorithms Theoretical Foundations and Applications to Computational Imaging

    CERN Document Server

    Barneva, Reneta

    2012-01-01

    Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.

  20. Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

    KAUST Repository

    Abubeker, Jewahir Ali

    2011-05-14

    This paper is devoted to the consideration of an algorithm for sequential optimization of paths in directed graphs relative to di_erent cost functions. The considered algorithm is based on an extension of dynamic programming which allows to represent the initial set of paths and the set of optimal paths after each application of optimization procedure in the form of a directed acyclic graph.

  1. Cartesian product of hypergraphs: properties and algorithms

    Directory of Open Access Journals (Sweden)

    Alain Bretto

    2009-09-01

    Full Text Available Cartesian products of graphs have been studied extensively since the 1960s. They make it possible to decrease the algorithmic complexity of problems by using the factorization of the product. Hypergraphs were introduced as a generalization of graphs and the definition of Cartesian products extends naturally to them. In this paper, we give new properties and algorithms concerning coloring aspects of Cartesian products of hypergraphs. We also extend a classical prime factorization algorithm initially designed for graphs to connected conformal hypergraphs using 2-sections of hypergraphs.

  2. Quick Mining of Isomorphic Exact Large Patterns from Large Graphs

    KAUST Repository

    Almasri, Islam

    2014-12-01

    The applications of the sub graph isomorphism search are growing with the growing number of areas that model their systems using graphs or networks. Specifically, many biological systems, such as protein interaction networks, molecular structures and protein contact maps, are modeled as graphs. The sub graph isomorphism search is concerned with finding all sub graphs that are isomorphic to a relevant query graph, the existence of such sub graphs can reflect on the characteristics of the modeled system. The most computationally expensive step in the search for isomorphic sub graphs is the backtracking algorithm that traverses the nodes of the target graph. In this paper, we propose a pruning approach that is inspired by the minimum remaining value heuristic that achieves greater scalability over large query and target graphs. Our testing on various biological networks shows that performance enhancement of our approach over existing state-of-the-art approaches varies between 6x and 53x. © 2014 IEEE.

  3. Quick Mining of Isomorphic Exact Large Patterns from Large Graphs

    KAUST Repository

    Almasri, Islam; Gao, Xin; Fedoroff, Nina V.

    2014-01-01

    The applications of the sub graph isomorphism search are growing with the growing number of areas that model their systems using graphs or networks. Specifically, many biological systems, such as protein interaction networks, molecular structures and protein contact maps, are modeled as graphs. The sub graph isomorphism search is concerned with finding all sub graphs that are isomorphic to a relevant query graph, the existence of such sub graphs can reflect on the characteristics of the modeled system. The most computationally expensive step in the search for isomorphic sub graphs is the backtracking algorithm that traverses the nodes of the target graph. In this paper, we propose a pruning approach that is inspired by the minimum remaining value heuristic that achieves greater scalability over large query and target graphs. Our testing on various biological networks shows that performance enhancement of our approach over existing state-of-the-art approaches varies between 6x and 53x. © 2014 IEEE.

  4. HaVec: An Efficient de Bruijn Graph Construction Algorithm for Genome Assembly

    Directory of Open Access Journals (Sweden)

    Md Mahfuzer Rahman

    2017-01-01

    Full Text Available Background. The rapid advancement of sequencing technologies has made it possible to regularly produce millions of high-quality reads from the DNA samples in the sequencing laboratories. To this end, the de Bruijn graph is a popular data structure in the genome assembly literature for efficient representation and processing of data. Due to the number of nodes in a de Bruijn graph, the main barrier here is the memory and runtime. Therefore, this area has received significant attention in contemporary literature. Results. In this paper, we present an approach called HaVec that attempts to achieve a balance between the memory consumption and the running time. HaVec uses a hash table along with an auxiliary vector data structure to store the de Bruijn graph thereby improving the total memory usage and the running time. A critical and noteworthy feature of HaVec is that it exhibits no false positive error. Conclusions. In general, the graph construction procedure takes the major share of the time involved in an assembly process. HaVec can be seen as a significant advancement in this aspect. We anticipate that HaVec will be extremely useful in the de Bruijn graph-based genome assembly.

  5. Local search for Steiner tree problems in graphs

    NARCIS (Netherlands)

    Verhoeven, M.G.A.; Severens, M.E.M.; Aarts, E.H.L.; Rayward-Smith, V.J.; Reeves, C.R.; Smith, G.D.

    1996-01-01

    We present a local search algorithm for the Steiner tree problem in graphs, which uses a neighbourhood in which paths in a steiner tree are exchanged. The exchange function of this neigbourhood is based on multiple-source shortest path algorithm. We present computational results for a known

  6. On some interconnections between combinatorial optimization and extremal graph theory

    Directory of Open Access Journals (Sweden)

    Cvetković Dragoš M.

    2004-01-01

    Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.

  7. Structuring heterogeneous biological information using fuzzy clustering of k-partite graphs

    Directory of Open Access Journals (Sweden)

    Theis Fabian J

    2010-10-01

    Full Text Available Abstract Background Extensive and automated data integration in bioinformatics facilitates the construction of large, complex biological networks. However, the challenge lies in the interpretation of these networks. While most research focuses on the unipartite or bipartite case, we address the more general but common situation of k-partite graphs. These graphs contain k different node types and links are only allowed between nodes of different types. In order to reveal their structural organization and describe the contained information in a more coarse-grained fashion, we ask how to detect clusters within each node type. Results Since entities in biological networks regularly have more than one function and hence participate in more than one cluster, we developed a k-partite graph partitioning algorithm that allows for overlapping (fuzzy clusters. It determines for each node a degree of membership to each cluster. Moreover, the algorithm estimates a weighted k-partite graph that connects the extracted clusters. Our method is fast and efficient, mimicking the multiplicative update rules commonly employed in algorithms for non-negative matrix factorization. It facilitates the decomposition of networks on a chosen scale and therefore allows for analysis and interpretation of structures on various resolution levels. Applying our algorithm to a tripartite disease-gene-protein complex network, we were able to structure this graph on a large scale into clusters that are functionally correlated and biologically meaningful. Locally, smaller clusters enabled reclassification or annotation of the clusters' elements. We exemplified this for the transcription factor MECP2. Conclusions In order to cope with the overwhelming amount of information available from biomedical literature, we need to tackle the challenge of finding structures in large networks with nodes of multiple types. To this end, we presented a novel fuzzy k-partite graph partitioning

  8. Sound Control-Flow Graph Extraction for Java Programs with Exceptions

    NARCIS (Netherlands)

    Amighi, A.; de Carvalho Gomes, Pedro; Gurov, Dilian; Huisman, Marieke; Eleftherakis, George; Hinchey, Mike; Holcombe, Mike

    2012-01-01

    We present an algorithm to extract control-flow graphs from Java bytecode, considering exceptional flows. We then establish its correctness: the behavior of the extracted graphs is shown to be a sound over-approximation of the behavior of the original programs. Thus, any temporal safety property

  9. Provably Correct Control-Flow Graphs from Java Programs with Exceptions

    NARCIS (Netherlands)

    Amighi, A.; de Carvalho Gomes, Pedro; Huisman, Marieke

    2011-01-01

    We present an algorithm to extract flow graphs from Java bytecode, focusing on exceptional control flows. We prove its correctness, meaning that the behaviour of the extracted control-flow graph is an over-approximation of the behaviour of the original program. Thus any safety property that holds

  10. Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Bergbauer, Christoph

    2009-06-11

    The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

  11. Combinatorial and geometric aspects of Feynman graphs and Feynman integrals

    International Nuclear Information System (INIS)

    Bergbauer, Christoph

    2009-01-01

    The integrals associated to Feynman graphs must have been a source of frustration for particle physicists ever since. Indeed there is a delicate difference between being able to draw a Feynman graph and being able to compute the associated Feynman integral. Although perturbation theory has brought enormous breakthroughs, many physicists turned to more abstract developments in quantum field theory, looked for other ways to produce perturbational results, or left the field entirely. Nonetheless there is a significant number of physicists, computational and theoretical, who pursue the quest for concepts and algorithms to compute and understand those integrals to higher and higher orders. Their motivation is to help test the validity of the underlying physical theory. For a mathematician, Feynman graphs and their integrals provide a rich subject in their own right, independent of their computability. It was only recently though that the work of Bloch, Esnault and Kreimer has brought a growing interest of mathematicians from various disciplines to the subject. In fact it opened up a completely new direction of research: a motivic interpretation of Feynman graphs that unites their combinatorial, geometric and arithmetic aspects. This idea had been in the air for a while, based on computational results of Broadhurst and Kreimer, and on a theorem of Belkale and Brosnan related to a conjecture of Kontsevich about the generality of the underlying motives. A prerequisite for the motivic approach is a profound understanding of renormalization that was established less recently in a modern language by Connes and Kreimer. This dissertation studies the renormalization of Feynman graphs in position space using an adapted resolution of singularities, and makes two other contributions of mostly combinatorial nature to the subject. I hope this may serve as a reference for somebody who feels comfortable with the traditional position space literature and looks for a transition to the

  12. Gromov hyperbolicity in lexicographic product graphs

    Indian Academy of Sciences (India)

    41

    on the group [17]. The concept of hyperbolicity appears also in discrete mathematics, algorithms and networking. For .... graph (of a presentation with solvable word problem) there is an algorithm which allows to decide if it is ...... of Theorem 3.14, i.e., dG1◦{w}(Vp, [π(x)π(z)] ∪ [π(z)π(y)]) = δ(G1) with π the canonical projection.

  13. STRUCTURAL ANNOTATION OF EM IMAGES BY GRAPH CUT

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Hang; Auer, Manfred; Parvin, Bahram

    2009-05-08

    Biological images have the potential to reveal complex signatures that may not be amenable to morphological modeling in terms of shape, location, texture, and color. An effective analytical method is to characterize the composition of a specimen based on user-defined patterns of texture and contrast formation. However, such a simple requirement demands an improved model for stability and robustness. Here, an interactive computational model is introduced for learning patterns of interest by example. The learned patterns bound an active contour model in which the traditional gradient descent optimization is replaced by the more efficient optimization of the graph cut methods. First, the energy function is defined according to the curve evolution. Next, a graph is constructed with weighted edges on the energy function and is optimized with the graph cut algorithm. As a result, the method combines the advantages of the level set method and graph cut algorithm, i.e.,"topological" invariance and computational efficiency. The technique is extended to the multi-phase segmentation problem; the method is validated on synthetic images and then applied to specimens imaged by transmission electron microscopy(TEM).

  14. A sampling algorithm for segregation analysis

    Directory of Open Access Journals (Sweden)

    Henshall John

    2001-11-01

    Full Text Available Abstract Methods for detecting Quantitative Trait Loci (QTL without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated.

  15. Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

    International Nuclear Information System (INIS)

    Azad, Ariful; Buluc, Aydn; Pothen, Alex

    2016-01-01

    It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting path is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.

  16. Identifying patients with Alzheimer's disease using resting-state fMRI and graph theory.

    Science.gov (United States)

    Khazaee, Ali; Ebrahimzadeh, Ata; Babajani-Feremi, Abbas

    2015-11-01

    Study of brain network on the basis of resting-state functional magnetic resonance imaging (fMRI) has provided promising results to investigate changes in connectivity among different brain regions because of diseases. Graph theory can efficiently characterize different aspects of the brain network by calculating measures of integration and segregation. In this study, we combine graph theoretical approaches with advanced machine learning methods to study functional brain network alteration in patients with Alzheimer's disease (AD). Support vector machine (SVM) was used to explore the ability of graph measures in diagnosis of AD. We applied our method on the resting-state fMRI data of twenty patients with AD and twenty age and gender matched healthy subjects. The data were preprocessed and each subject's graph was constructed by parcellation of the whole brain into 90 distinct regions using the automated anatomical labeling (AAL) atlas. The graph measures were then calculated and used as the discriminating features. Extracted network-based features were fed to different feature selection algorithms to choose most significant features. In addition to the machine learning approach, statistical analysis was performed on connectivity matrices to find altered connectivity patterns in patients with AD. Using the selected features, we were able to accurately classify patients with AD from healthy subjects with accuracy of 100%. Results of this study show that pattern recognition and graph of brain network, on the basis of the resting state fMRI data, can efficiently assist in the diagnosis of AD. Classification based on the resting-state fMRI can be used as a non-invasive and automatic tool to diagnosis of Alzheimer's disease. Copyright © 2015 International Federation of Clinical Neurophysiology. All rights reserved.

  17. Empirical Comparison of Graph-based Recommendation Engines for an Apps Ecosystem

    Directory of Open Access Journals (Sweden)

    Luis F. Chiroque

    2015-03-01

    Full Text Available Recommendation engines (RE are becoming highly popular, e.g., in the area of e-commerce. A RE offers new items (products or content to users based on their profile and historical data. The most popular algorithms used in RE are based on collaborative filtering. This technique makes recommendations based on the past behavior of other users and the similarity between users and items. In this paper we have evaluated the performance of several RE based on the properties of the networks formed by users and items. The RE use in a novel way graph theoretic concepts like edges weights or network flow. The evaluation has been conducted in a real environment (ecosystem for recommending apps to smartphone users. The analysis of the results allows concluding that the effectiveness of a RE can be improved if the age of the data, and if a global view of the data is considered. It also shows that graph-based RE are effective, but more experiments are required for a more accurate characterization of their properties.

  18. GAT: a graph-theoretical analysis toolbox for analyzing between-group differences in large-scale structural and functional brain networks.

    Science.gov (United States)

    Hosseini, S M Hadi; Hoeft, Fumiko; Kesler, Shelli R

    2012-01-01

    In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.

  19. GAT: a graph-theoretical analysis toolbox for analyzing between-group differences in large-scale structural and functional brain networks.

    Directory of Open Access Journals (Sweden)

    S M Hadi Hosseini

    Full Text Available In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC and functional data analyses (FDA, in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL and healthy matched Controls (CON. The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.

  20. OpenMP Parallelization and Optimization of Graph-based Machine Learning Algorithms

    Science.gov (United States)

    2016-05-01

    Understanding Application Data Movement Characteristics using Intel VTune Amplifier and Software Development Emulator tools, Intel Xeon Phi User Group...sured by a summation of the weights along the graph cut) for this problem. This is equivalent to assigning a scalar or vector value ui to each i th data...graph Laplacian [9]. By projecting all vectors onto this sub-eigenspace, the iteration step reduces to a simple coefficient update. 2.2 Semi-supervised

  1. Multidimensional Brain MRI segmentation using graph cuts

    International Nuclear Information System (INIS)

    Lecoeur, Jeremy

    2010-01-01

    This thesis deals with the segmentation of multimodal brain MRIs by graph cuts method. First, we propose a method that utilizes three MRI modalities by merging them. The border information given by the spectral gradient is then challenged by a region information, given by the seeds selected by the user, using a graph cut algorithm. Then, we propose three enhancements of this method. The first consists in finding an optimal spectral space because the spectral gradient is based on natural images and then inadequate for multimodal medical images. This results in a learning based segmentation method. We then explore the automation of the graph cut method. Here, the various pieces of information usually given by the user are inferred from a robust expectation-maximization algorithm. We show the performance of these two enhanced versions on multiple sclerosis lesions. Finally, we integrate atlases for the automatic segmentation of deep brain structures. These three new techniques show the adaptability of our method to various problems. Our different segmentation methods are better than most of nowadays techniques, speaking of computation time or segmentation accuracy. (authors)

  2. On the graph turnpike problem

    KAUST Repository

    Feder, Tomá s; Motwani, Rajeev

    2009-01-01

    Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.

  3. On the graph turnpike problem

    KAUST Repository

    Feder, Tomás

    2009-06-01

    Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.

  4. Contracting a planar graph efficiently

    DEFF Research Database (Denmark)

    Holm, Jacob; Italiano, Giuseppe F.; Karczmarz, Adam

    2017-01-01

    the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar...

  5. Equitable Colorings Of Corona Multiproducts Of Graphs

    Directory of Open Access Journals (Sweden)

    Furmánczyk Hanna

    2017-11-01

    Full Text Available A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by =(G. It is known that the problem of computation of =(G is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013 103–120].

  6. A Novel Efficient Graph Model for the Multiple Longest Common Subsequences (MLCS Problem

    Directory of Open Access Journals (Sweden)

    Zhan Peng

    2017-08-01

    Full Text Available Searching for the Multiple Longest Common Subsequences (MLCS of multiple sequences is a classical NP-hard problem, which has been used in many applications. One of the most effective exact approaches for the MLCS problem is based on dominant point graph, which is a kind of directed acyclic graph (DAG. However, the time and space efficiency of the leading dominant point graph based approaches is still unsatisfactory: constructing the dominated point graph used by these approaches requires a huge amount of time and space, which hinders the applications of these approaches to large-scale and long sequences. To address this issue, in this paper, we propose a new time and space efficient graph model called the Leveled-DAG for the MLCS problem. The Leveled-DAG can timely eliminate all the nodes in the graph that cannot contribute to the construction of MLCS during constructing. At any moment, only the current level and some previously generated nodes in the graph need to be kept in memory, which can greatly reduce the memory consumption. Also, the final graph contains only one node in which all of the wanted MLCS are saved, thus, no additional operations for searching the MLCS are needed. The experiments are conducted on real biological sequences with different numbers and lengths respectively, and the proposed algorithm is compared with three state-of-the-art algorithms. The experimental results show that the time and space needed for the Leveled-DAG approach are smaller than those for the compared algorithms especially on large-scale and long sequences.

  7. Exploring the brains of Baduk (Go experts: gray matter morphometry, resting-state functional connectivity, and graph theoretical analysis

    Directory of Open Access Journals (Sweden)

    Wi Hoon eJung

    2013-10-01

    Full Text Available One major characteristic of experts is intuitive judgment, which is an automatic process whereby patterns stored in memory through long-term training are recognized. Indeed, long-term training may influence brain structure and function. A recent study revealed that chess experts at rest showed differences in structure and functional connectivity (FC in the head of caudate, which is associated with rapid best next-move generation. However, less is known about the structure and function of the brains of Baduk experts compared with those of experts in other strategy games. Therefore, we performed voxel-based morphometry and FC analyses in Baduk experts to investigate structural brain differences and to clarify the influence of these differences on functional interactions. We also conducted graph theoretical analysis to explore the topological organization of whole-brain functional networks. Compared to novices, Baduk experts exhibited decreased and increased gray matter volume in the amygdala and nucleus accumbens, respectively. We also found increased FC between the amygdala and medial orbitofrontal cortex and decreased FC between the nucleus accumbens and medial prefrontal cortex. Further graph theoretical analysis revealed differences in measures of the integration of the network and in the regional nodal characteristics of various brain regions activated during Baduk. This study provides evidence for structural and functional differences as well as altered topological organization of the whole-brain functional networks in Baduk experts. Our findings also offer novel suggestions about the cognitive mechanisms behind Baduk expertise, which involves intuitive decision-making mediated by somatic marker circuitry and visuospatial processing.

  8. Skin Segmentation Based on Graph Cuts

    Institute of Scientific and Technical Information of China (English)

    HU Zhilan; WANG Guijin; LIN Xinggang; YAN Hong

    2009-01-01

    Skin segmentation is widely used in many computer vision tasks to improve automated visualiza-tion. This paper presents a graph cuts algorithm to segment arbitrary skin regions from images. The detected face is used to determine the foreground skin seeds and the background non-skin seeds with the color probability distributions for the foreground represented by a single Gaussian model and for the background by a Gaussian mixture model. The probability distribution of the image is used for noise suppression to alle-viate the influence of the background regions having skin-like colors. Finally, the skin is segmented by graph cuts, with the regional parameter y optimally selected to adapt to different images. Tests of the algorithm on many real wodd photographs show that the scheme accurately segments skin regions and is robust against illumination variations, individual skin variations, and cluttered backgrounds.

  9. Scalable Parallel Distributed Coprocessor System for Graph Searching Problems with Massive Data

    Directory of Open Access Journals (Sweden)

    Wanrong Huang

    2017-01-01

    Full Text Available The Internet applications, such as network searching, electronic commerce, and modern medical applications, produce and process massive data. Considerable data parallelism exists in computation processes of data-intensive applications. A traversal algorithm, breadth-first search (BFS, is fundamental in many graph processing applications and metrics when a graph grows in scale. A variety of scientific programming methods have been proposed for accelerating and parallelizing BFS because of the poor temporal and spatial locality caused by inherent irregular memory access patterns. However, new parallel hardware could provide better improvement for scientific methods. To address small-world graph problems, we propose a scalable and novel field-programmable gate array-based heterogeneous multicore system for scientific programming. The core is multithread for streaming processing. And the communication network InfiniBand is adopted for scalability. We design a binary search algorithm to address mapping to unify all processor addresses. Within the limits permitted by the Graph500 test bench after 1D parallel hybrid BFS algorithm testing, our 8-core and 8-thread-per-core system achieved superior performance and efficiency compared with the prior work under the same degree of parallelism. Our system is efficient not as a special acceleration unit but as a processor platform that deals with graph searching applications.

  10. Whole Genome Phylogenetic Tree Reconstruction using Colored de Bruijn Graphs

    OpenAIRE

    Lyman, Cole

    2017-01-01

    We present kleuren, a novel assembly-free method to reconstruct phylogenetic trees using the Colored de Bruijn Graph. kleuren works by constructing the Colored de Bruijn Graph and then traversing it, finding bubble structures in the graph that provide phylogenetic signal. The bubbles are then aligned and concatenated to form a supermatrix, from which a phylogenetic tree is inferred. We introduce the algorithm that kleuren uses to accomplish this task, and show its performance on reconstructin...

  11. Novel multiple criteria decision making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs

    OpenAIRE

    Muhammad, Akram; Musavarah, Sarwar

    2016-01-01

    In this research study, we introduce the concept of bipolar neutrosophic graphs. We present the dominating and independent sets of bipolar neutrosophic graphs. We describe novel multiple criteria decision making methods based on bipolar neutrosophic sets and bipolar neutrosophic graphs. We also develop an algorithm for computing domination in bipolar neutrosophic graphs.

  12. The Reduction of Directed Cyclic Graph for Task Assignment Problem

    Directory of Open Access Journals (Sweden)

    Ariffin W.N.M.

    2018-01-01

    Full Text Available In this paper, a directed cyclic graph (DCG is proposed as the task graph. It is undesirable and impossible to complete the task according to the constraints if the cycle exists. Therefore, an effort should be done in order to eliminate the cycle to obtain a directed acyclic graph (DAG, so that the minimum amount of time required for the entire task can be found. The technique of reducing the complexity of the directed cyclic graph to a directed acyclic graph by reversing the orientation of the path is the main contribution of this study. The algorithm was coded using Java programming and consistently produced good assignment and task schedule.

  13. Fully Automated Segmentation of Fluid/Cyst Regions in Optical Coherence Tomography Images With Diabetic Macular Edema Using Neutrosophic Sets and Graph Algorithms.

    Science.gov (United States)

    Rashno, Abdolreza; Koozekanani, Dara D; Drayna, Paul M; Nazari, Behzad; Sadri, Saeed; Rabbani, Hossein; Parhi, Keshab K

    2018-05-01

    This paper presents a fully automated algorithm to segment fluid-associated (fluid-filled) and cyst regions in optical coherence tomography (OCT) retina images of subjects with diabetic macular edema. The OCT image is segmented using a novel neutrosophic transformation and a graph-based shortest path method. In neutrosophic domain, an image is transformed into three sets: (true), (indeterminate) that represents noise, and (false). This paper makes four key contributions. First, a new method is introduced to compute the indeterminacy set , and a new -correction operation is introduced to compute the set in neutrosophic domain. Second, a graph shortest-path method is applied in neutrosophic domain to segment the inner limiting membrane and the retinal pigment epithelium as regions of interest (ROI) and outer plexiform layer and inner segment myeloid as middle layers using a novel definition of the edge weights . Third, a new cost function for cluster-based fluid/cyst segmentation in ROI is presented which also includes a novel approach in estimating the number of clusters in an automated manner. Fourth, the final fluid regions are achieved by ignoring very small regions and the regions between middle layers. The proposed method is evaluated using two publicly available datasets: Duke, Optima, and a third local dataset from the UMN clinic which is available online. The proposed algorithm outperforms the previously proposed Duke algorithm by 8% with respect to the dice coefficient and by 5% with respect to precision on the Duke dataset, while achieving about the same sensitivity. Also, the proposed algorithm outperforms a prior method for Optima dataset by 6%, 22%, and 23% with respect to the dice coefficient, sensitivity, and precision, respectively. Finally, the proposed algorithm also achieves sensitivity of 67.3%, 88.8%, and 76.7%, for the Duke, Optima, and the university of minnesota (UMN) datasets, respectively.

  14. MoleculaRnetworks: an integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation.

    Science.gov (United States)

    Mooney, Barbara Logan; Corrales, L René; Clark, Aurora E

    2012-03-30

    This work discusses scripts for processing molecular simulations data written using the software package R: A Language and Environment for Statistical Computing. These scripts, named moleculaRnetworks, are intended for the geometric and solvent network analysis of aqueous solutes and can be extended to other H-bonded solvents. New algorithms, several of which are based on graph theory, that interrogate the solvent environment about a solute are presented and described. This includes a novel method for identifying the geometric shape adopted by the solvent in the immediate vicinity of the solute and an exploratory approach for describing H-bonding, both based on the PageRank algorithm of Google search fame. The moleculaRnetworks codes include a preprocessor, which distills simulation trajectories into physicochemical data arrays, and an interactive analysis script that enables statistical, trend, and correlation analysis, and other data mining. The goal of these scripts is to increase access to the wealth of structural and dynamical information that can be obtained from molecular simulations. Copyright © 2012 Wiley Periodicals, Inc.

  15. Radioelement decay schemes and equivalent graphs: formulae generated by algorithm for radioelement detection

    International Nuclear Information System (INIS)

    Becker, Antoine; Lame, Jacques; Le Gallic, Yves.

    1980-02-01

    In order to obtain a theoretical expression for the resultant uncertainty from a general relation concerning the detection of a radionuclide with a complex decay scheme, we seek to discuss here the necessary conditions for writing down such an expression. These conditions are: (1) determination, on a graph equivalent to the decay scheme concerned, of a classification into simple elementary paths between specified initial and final levels, so that an occurrence probability can be assigned to each independent decay route; (2) at least formal consideration of detector 'responses', not to a particular particle emission, but to each independent route as a whole; (3) hence the derivation of detection-selection formulae, in the apparent absence of instrumental dead time, which are especially concise and readable, and allow the formal separation of the factors arising from the geometry, the decay scheme, the detector efficiency and the parametric distribution [fr

  16. Quantum graphs with the Bethe-Sommerfeld property

    Czech Academy of Sciences Publication Activity Database

    Exner, Pavel; Turek, Ondřej

    2017-01-01

    Roč. 8, č. 3 (2017), s. 305-309 ISSN 2220-8054 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : periodic quantum graphs * gap number * delta-coupling * rectangular lattice graph * scale-invariant coupling * Bethe-Sommerfeld conjecture * golden mean Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

  17. An intelligent allocation algorithm for parallel processing

    Science.gov (United States)

    Carroll, Chester C.; Homaifar, Abdollah; Ananthram, Kishan G.

    1988-01-01

    The problem of allocating nodes of a program graph to processors in a parallel processing architecture is considered. The algorithm is based on critical path analysis, some allocation heuristics, and the execution granularity of nodes in a program graph. These factors, and the structure of interprocessor communication network, influence the allocation. To achieve realistic estimations of the executive durations of allocations, the algorithm considers the fact that nodes in a program graph have to communicate through varying numbers of tokens. Coarse and fine granularities have been implemented, with interprocessor token-communication duration, varying from zero up to values comparable to the execution durations of individual nodes. The effect on allocation of communication network structures is demonstrated by performing allocations for crossbar (non-blocking) and star (blocking) networks. The algorithm assumes the availability of as many processors as it needs for the optimal allocation of any program graph. Hence, the focus of allocation has been on varying token-communication durations rather than varying the number of processors. The algorithm always utilizes as many processors as necessary for the optimal allocation of any program graph, depending upon granularity and characteristics of the interprocessor communication network.

  18. Generating hierarchial scale-free graphs from fractals

    Energy Technology Data Exchange (ETDEWEB)

    Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)

    2011-08-15

    Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.

  19. Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

    KAUST Repository

    Mahayni, Malek A.

    2011-01-01

    developed to solve the optimal paths problem with different kinds of graphs. An algorithm that solves the problem of paths’ optimization in directed graphs relative to different cost functions is described in [1]. It follows an approach extended from

  20. Man-Made Object Extraction from Remote Sensing Imagery by Graph-Based Manifold Ranking

    Science.gov (United States)

    He, Y.; Wang, X.; Hu, X. Y.; Liu, S. H.

    2018-04-01

    The automatic extraction of man-made objects from remote sensing imagery is useful in many applications. This paper proposes an algorithm for extracting man-made objects automatically by integrating a graph model with the manifold ranking algorithm. Initially, we estimate a priori value of the man-made objects with the use of symmetric and contrast features. The graph model is established to represent the spatial relationships among pre-segmented superpixels, which are used as the graph nodes. Multiple characteristics, namely colour, texture and main direction, are used to compute the weights of the adjacent nodes. Manifold ranking effectively explores the relationships among all the nodes in the feature space as well as initial query assignment; thus, it is applied to generate a ranking map, which indicates the scores of the man-made objects. The man-made objects are then segmented on the basis of the ranking map. Two typical segmentation algorithms are compared with the proposed algorithm. Experimental results show that the proposed algorithm can extract man-made objects with high recognition rate and low omission rate.

  1. Learning Based Approach for Optimal Clustering of Distributed Program's Call Flow Graph

    Science.gov (United States)

    Abofathi, Yousef; Zarei, Bager; Parsa, Saeed

    Optimal clustering of call flow graph for reaching maximum concurrency in execution of distributable components is one of the NP-Complete problems. Learning automatas (LAs) are search tools which are used for solving many NP-Complete problems. In this paper a learning based algorithm is proposed to optimal clustering of call flow graph and appropriate distributing of programs in network level. The algorithm uses learning feature of LAs to search in state space. It has been shown that the speed of reaching to solution increases remarkably using LA in search process, and it also prevents algorithm from being trapped in local minimums. Experimental results show the superiority of proposed algorithm over others.

  2. Combining Vertex-centric Graph Processing with SPARQL for Large-scale RDF Data Analytics

    KAUST Repository

    Abdelaziz, Ibrahim

    2017-06-27

    Modern applications, such as drug repositioning, require sophisticated analytics on RDF graphs that combine structural queries with generic graph computations. Existing systems support either declarative SPARQL queries, or generic graph processing, but not both. We bridge the gap by introducing Spartex, a versatile framework for complex RDF analytics. Spartex extends SPARQL to support programs that combine seamlessly generic graph algorithms (e.g., PageRank, Shortest Paths, etc.) with SPARQL queries. Spartex builds on existing vertex-centric graph processing frameworks, such as Graphlab or Pregel. It implements a generic SPARQL operator as a vertex-centric program that interprets SPARQL queries and executes them efficiently using a built-in optimizer. In addition, any graph algorithm implemented in the underlying vertex-centric framework, can be executed in Spartex. We present various scenarios where our framework simplifies significantly the implementation of complex RDF data analytics programs. We demonstrate that Spartex scales to datasets with billions of edges, and show that our core SPARQL engine is at least as fast as the state-of-the-art specialized RDF engines. For complex analytical tasks that combine generic graph processing with SPARQL, Spartex is at least an order of magnitude faster than existing alternatives.

  3. A Parallel Approach for Frequent Subgraph Mining in a Single Large Graph Using Spark

    Directory of Open Access Journals (Sweden)

    Fengcai Qiao

    2018-02-01

    Full Text Available Frequent subgraph mining (FSM plays an important role in graph mining, attracting a great deal of attention in many areas, such as bioinformatics, web data mining and social networks. In this paper, we propose SSiGraM (Spark based Single Graph Mining, a Spark based parallel frequent subgraph mining algorithm in a single large graph. Aiming to approach the two computational challenges of FSM, we conduct the subgraph extension and support evaluation parallel across all the distributed cluster worker nodes. In addition, we also employ a heuristic search strategy and three novel optimizations: load balancing, pre-search pruning and top-down pruning in the support evaluation process, which significantly improve the performance. Extensive experiments with four different real-world datasets demonstrate that the proposed algorithm outperforms the existing GraMi (Graph Mining algorithm by an order of magnitude for all datasets and can work with a lower support threshold.

  4. Efficient and exact sampling of simple graphs with given arbitrary degree sequence.

    Directory of Open Access Journals (Sweden)

    Charo I Del Genio

    Full Text Available Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms or stub-matching based (the Configuration Model. Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large , and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.

  5. Aligning Biomolecular Networks Using Modular Graph Kernels

    Science.gov (United States)

    Towfic, Fadi; Greenlee, M. Heather West; Honavar, Vasant

    Comparative analysis of biomolecular networks constructed using measurements from different conditions, tissues, and organisms offer a powerful approach to understanding the structure, function, dynamics, and evolution of complex biological systems. We explore a class of algorithms for aligning large biomolecular networks by breaking down such networks into subgraphs and computing the alignment of the networks based on the alignment of their subgraphs. The resulting subnetworks are compared using graph kernels as scoring functions. We provide implementations of the resulting algorithms as part of BiNA, an open source biomolecular network alignment toolkit. Our experiments using Drosophila melanogaster, Saccharomyces cerevisiae, Mus musculus and Homo sapiens protein-protein interaction networks extracted from the DIP repository of protein-protein interaction data demonstrate that the performance of the proposed algorithms (as measured by % GO term enrichment of subnetworks identified by the alignment) is competitive with some of the state-of-the-art algorithms for pair-wise alignment of large protein-protein interaction networks. Our results also show that the inter-species similarity scores computed based on graph kernels can be used to cluster the species into a species tree that is consistent with the known phylogenetic relationships among the species.

  6. Multiple Kernel Learning for adaptive graph regularized nonnegative matrix factorization

    KAUST Repository

    Wang, Jim Jing-Yan; AbdulJabbar, Mustafa Abdulmajeed

    2012-01-01

    Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of non-negative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation, which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.

  7. Structural modeling and analysis of an effluent treatment process for electroplating--a graph theoretic approach.

    Science.gov (United States)

    Kumar, Abhishek; Clement, Shibu; Agrawal, V P

    2010-07-15

    An attempt is made to address a few ecological and environment issues by developing different structural models for effluent treatment system for electroplating. The effluent treatment system is defined with the help of different subsystems contributing to waste minimization. Hierarchical tree and block diagram showing all possible interactions among subsystems are proposed. These non-mathematical diagrams are converted into mathematical models for design improvement, analysis, comparison, storage retrieval and commercially off-the-shelf purchases of different subsystems. This is achieved by developing graph theoretic model, matrix models and variable permanent function model. Analysis is carried out by permanent function, hierarchical tree and block diagram methods. Storage and retrieval is done using matrix models. The methodology is illustrated with the help of an example. Benefits to the electroplaters/end user are identified. 2010 Elsevier B.V. All rights reserved.

  8. Fully-automated approach to hippocampus segmentation using a graph-cuts algorithm combined with atlas-based segmentation and morphological opening.

    Science.gov (United States)

    Kwak, Kichang; Yoon, Uicheul; Lee, Dong-Kyun; Kim, Geon Ha; Seo, Sang Won; Na, Duk L; Shim, Hack-Joon; Lee, Jong-Min

    2013-09-01

    The hippocampus has been known to be an important structure as a biomarker for Alzheimer's disease (AD) and other neurological and psychiatric diseases. However, it requires accurate, robust and reproducible delineation of hippocampal structures. In this study, an automated hippocampal segmentation method based on a graph-cuts algorithm combined with atlas-based segmentation and morphological opening was proposed. First of all, the atlas-based segmentation was applied to define initial hippocampal region for a priori information on graph-cuts. The definition of initial seeds was further elaborated by incorporating estimation of partial volume probabilities at each voxel. Finally, morphological opening was applied to reduce false positive of the result processed by graph-cuts. In the experiments with twenty-seven healthy normal subjects, the proposed method showed more reliable results (similarity index=0.81±0.03) than the conventional atlas-based segmentation method (0.72±0.04). Also as for segmentation accuracy which is measured in terms of the ratios of false positive and false negative, the proposed method (precision=0.76±0.04, recall=0.86±0.05) produced lower ratios than the conventional methods (0.73±0.05, 0.72±0.06) demonstrating its plausibility for accurate, robust and reliable segmentation of hippocampus. Copyright © 2013 Elsevier Inc. All rights reserved.

  9. Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis

    KAUST Repository

    Kuźnik, Krzysztof; Paszyński, Maciej; Calo, Victor M.

    2012-01-01

    at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar

  10. Deciding the On-line Chromatic Number of a Graph with Pre-coloring is PSPACE-complete

    DEFF Research Database (Denmark)

    Kudahl, Christian

    2015-01-01

    In an on-line coloring, the vertices of a graph are revealed one by one. An algorithm assigns a color to each vertex after it is revealed. When a vertex is revealed, it is also revealed which of the previous vertices it is adjacent to. The on-line chromatic number of a graph, G, is the smallest...... number of colors an algorithm will need when on-line-coloring G. The algorithm may know G, but not the order in which the vertices are revealed. The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE-complete....

  11. The Graph Laplacian and the Dynamics of Complex Networks

    Energy Technology Data Exchange (ETDEWEB)

    Thulasidasan, Sunil [Los Alamos National Laboratory

    2012-06-11

    In this talk, we explore the structure of networks from a spectral graph-theoretic perspective by analyzing the properties of the Laplacian matrix associated with the graph induced by a network. We will see how the eigenvalues of the graph Laplacian relate to the underlying network structure and dynamics and provides insight into a phenomenon frequently observed in real world networks - the emergence of collective behavior from purely local interactions seen in the coordinated motion of animals and phase transitions in biological networks, to name a few.

  12. Semi-Supervised Tensor-Based Graph Embedding Learning and Its Application to Visual Discriminant Tracking.

    Science.gov (United States)

    Hu, Weiming; Gao, Jin; Xing, Junliang; Zhang, Chao; Maybank, Stephen

    2017-01-01

    An appearance model adaptable to changes in object appearance is critical in visual object tracking. In this paper, we treat an image patch as a two-order tensor which preserves the original image structure. We design two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding space. In order to encode more discriminant information in the embedding space, we propose a transfer-learning- based semi-supervised strategy to iteratively adjust the embedding space into which discriminative information obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph embedding learning algorithm to visual tracking. The new tracking algorithm captures an object's appearance characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm.

  13. Performance Analysis of Evolutionary Algorithms for Steiner Tree Problems.

    Science.gov (United States)

    Lai, Xinsheng; Zhou, Yuren; Xia, Xiaoyun; Zhang, Qingfu

    2017-01-01

    The Steiner tree problem (STP) aims to determine some Steiner nodes such that the minimum spanning tree over these Steiner nodes and a given set of special nodes has the minimum weight, which is NP-hard. STP includes several important cases. The Steiner tree problem in graphs (GSTP) is one of them. Many heuristics have been proposed for STP, and some of them have proved to be performance guarantee approximation algorithms for this problem. Since evolutionary algorithms (EAs) are general and popular randomized heuristics, it is significant to investigate the performance of EAs for STP. Several empirical investigations have shown that EAs are efficient for STP. However, up to now, there is no theoretical work on the performance of EAs for STP. In this article, we reveal that the (1+1) EA achieves 3/2-approximation ratio for STP in a special class of quasi-bipartite graphs in expected runtime [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are, respectively, the number of Steiner nodes, the number of special nodes, and the largest weight among all edges in the input graph. We also show that the (1+1) EA is better than two other heuristics on two GSTP instances, and the (1+1) EA may be inefficient on a constructed GSTP instance.

  14. Provably correct control flow graphs from Java bytecode programs with exceptions

    NARCIS (Netherlands)

    Amighi, A.; de Carvalho Gomes, Pedro; Gurov, Dilian; Huisman, Marieke

    2016-01-01

    We present an algorithm for extracting control flow graphs from Java bytecode that captures normal as well as exceptional control flow. We prove its correctness, in the sense that the behaviour of the extracted control flow graph is a sound over-approximation of the behaviour of the original

  15. Computing the dilation of edge-augmented graphs in metric spaces

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    2010-01-01

    Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how...... to improve the running time to O(n3logn) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G{(u,v)} for every pair of distinct vertices u and v....

  16. A graph model for opportunistic network coding

    KAUST Repository

    Sorour, Sameh

    2015-08-12

    © 2015 IEEE. Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase in complexity. In this paper, we design a simple IDNC-like graph model for a specific subclass of ONC, by introducing a more generalized definition of its vertices and the notion of vertex aggregation in order to represent the storage of non-instantly-decodable packets in ONC. Based on this representation, we determine the set of pairwise vertex adjacency conditions that can populate this graph with edges so as to guarantee decodability or aggregation for the vertices of each clique in this graph. We then develop the algorithmic procedures that can be applied on the designed graph model to optimize any performance metric for this ONC subclass. A case study on reducing the completion time shows that the proposed framework improves on the performance of IDNC and gets very close to the optimal performance.

  17. Learning a Nonnegative Sparse Graph for Linear Regression.

    Science.gov (United States)

    Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung

    2015-09-01

    Previous graph-based semisupervised learning (G-SSL) methods have the following drawbacks: 1) they usually predefine the graph structure and then use it to perform label prediction, which cannot guarantee an overall optimum and 2) they only focus on the label prediction or the graph structure construction but are not competent in handling new samples. To this end, a novel nonnegative sparse graph (NNSG) learning method was first proposed. Then, both the label prediction and projection learning were integrated into linear regression. Finally, the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks. Therefore, a novel method, named learning a NNSG for linear regression was presented, in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum. In the learning process, the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples. An effective algorithm was designed to solve the corresponding optimization problem with fast convergence. Furthermore, NNSG provides a unified perceptiveness for a number of graph-based learning methods and linear regression methods. The experimental results showed that NNSG can obtain very high classification accuracy and greatly outperforms conventional G-SSL methods, especially some conventional graph construction methods.

  18. Multi-Agent Pathfinding with n Agents on Graphs with n Vertices

    DEFF Research Database (Denmark)

    Förster, Klaus-Tycho; Groner, Linus; Hoefler, Torsten

    2017-01-01

    We investigate the multi-agent pathfinding (MAPF) problem with $n$ agents on graphs with $n$ vertices: Each agent has a unique start and goal vertex, with the objective of moving all agents in parallel movements to their goal s.t.~each vertex and each edge may only be used by one agent at a time....... We give a combinatorial classification of all graphs where this problem is solvable in general, including cases where the solvability depends on the initial agent placement. Furthermore, we present an algorithm solving the MAPF problem in our setting, requiring O(n²) rounds, or O(n³) moves...... of individual agents. Complementing these results, we show that there are graphs where Omega(n²) rounds and Omega(n³) moves are required for any algorithm....

  19. Efficient Implementation of Nested-Loop Multimedia Algorithms

    Directory of Open Access Journals (Sweden)

    Kittitornkun Surin

    2001-01-01

    Full Text Available A novel dependence graph representation called the multiple-order dependence graph for nested-loop formulated multimedia signal processing algorithms is proposed. It allows a concise representation of an entire family of dependence graphs. This powerful representation facilitates the development of innovative implementation approach for nested-loop formulated multimedia algorithms such as motion estimation, matrix-matrix product, 2D linear transform, and others. In particular, algebraic linear mapping (assignment and scheduling methodology can be applied to implement such algorithms on an array of simple-processing elements. The feasibility of this new approach is demonstrated in three major target architectures: application-specific integrated circuit (ASIC, field programmable gate array (FPGA, and a programmable clustered VLIW processor.

  20. Identifying Vulnerabilities and Hardening Attack Graphs for Networked Systems

    Energy Technology Data Exchange (ETDEWEB)

    Saha, Sudip; Vullinati, Anil K.; Halappanavar, Mahantesh; Chatterjee, Samrat

    2016-09-15

    We investigate efficient security control methods for protecting against vulnerabilities in networked systems. A large number of interdependent vulnerabilities typically exist in the computing nodes of a cyber-system; as vulnerabilities get exploited, starting from low level ones, they open up the doors to more critical vulnerabilities. These cannot be understood just by a topological analysis of the network, and we use the attack graph abstraction of Dewri et al. to study these problems. In contrast to earlier approaches based on heuristics and evolutionary algorithms, we study rigorous methods for quantifying the inherent vulnerability and hardening cost for the system. We develop algorithms with provable approximation guarantees, and evaluate them for real and synthetic attack graphs.

  1. Spectral clustering and biclustering learning large graphs and contingency tables

    CERN Document Server

    Bolla, Marianna

    2013-01-01

    Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, mult

  2. An Expert System toward Buiding An Earth Science Knowledge Graph

    Science.gov (United States)

    Zhang, J.; Duan, X.; Ramachandran, R.; Lee, T. J.; Bao, Q.; Gatlin, P. N.; Maskey, M.

    2017-12-01

    In this ongoing work, we aim to build foundations of Cognitive Computing for Earth Science research. The goal of our project is to develop an end-to-end automated methodology for incrementally constructing Knowledge Graphs for Earth Science (KG4ES). These knowledge graphs can then serve as the foundational components for building cognitive systems in Earth science, enabling researchers to uncover new patterns and hypotheses that are virtually impossible to identify today. In addition, this research focuses on developing mining algorithms needed to exploit these constructed knowledge graphs. As such, these graphs will free knowledge from publications that are generated in a very linear, deterministic manner, and structure knowledge in a way that users can both interact and connect with relevant pieces of information. Our major contributions are two-fold. First, we have developed an end-to-end methodology for constructing Knowledge Graphs for Earth Science (KG4ES) using existing corpus of journal papers and reports. One of the key challenges in any machine learning, especially deep learning applications, is the need for robust and large training datasets. We have developed techniques capable of automatically retraining models and incrementally building and updating KG4ES, based on ever evolving training data. We also adopt the evaluation instrument based on common research methodologies used in Earth science research, especially in Atmospheric Science. Second, we have developed an algorithm to infer new knowledge that can exploit the constructed KG4ES. In more detail, we have developed a network prediction algorithm aiming to explore and predict possible new connections in the KG4ES and aid in new knowledge discovery.

  3. Using graph approach for managing connectivity in integrative landscape modelling

    Science.gov (United States)

    Rabotin, Michael; Fabre, Jean-Christophe; Libres, Aline; Lagacherie, Philippe; Crevoisier, David; Moussa, Roger

    2013-04-01

    In cultivated landscapes, a lot of landscape elements such as field boundaries, ditches or banks strongly impact water flows, mass and energy fluxes. At the watershed scale, these impacts are strongly conditionned by the connectivity of these landscape elements. An accurate representation of these elements and of their complex spatial arrangements is therefore of great importance for modelling and predicting these impacts.We developped in the framework of the OpenFLUID platform (Software Environment for Modelling Fluxes in Landscapes) a digital landscape representation that takes into account the spatial variabilities and connectivities of diverse landscape elements through the application of the graph theory concepts. The proposed landscape representation consider spatial units connected together to represent the flux exchanges or any other information exchanges. Each spatial unit of the landscape is represented as a node of a graph and relations between units as graph connections. The connections are of two types - parent-child connection and up/downstream connection - which allows OpenFLUID to handle hierarchical graphs. Connections can also carry informations and graph evolution during simulation is possible (connections or elements modifications). This graph approach allows a better genericity on landscape representation, a management of complex connections and facilitate development of new landscape representation algorithms. Graph management is fully operational in OpenFLUID for developers or modelers ; and several graph tools are available such as graph traversal algorithms or graph displays. Graph representation can be managed i) manually by the user (for example in simple catchments) through XML-based files in easily editable and readable format or ii) by using methods of the OpenFLUID-landr library which is an OpenFLUID library relying on common open-source spatial libraries (ogr vector, geos topologic vector and gdal raster libraries). Open

  4. SPECIAL LIBRARIES OF FRAGMENTS OF ALGORITHMIC NETWORKS TO AUTOMATE THE DEVELOPMENT OF ALGORITHMIC MODELS

    Directory of Open Access Journals (Sweden)

    V. E. Marley

    2015-01-01

    Full Text Available Summary. The concept of algorithmic models appeared from the algorithmic approach in which the simulated object, the phenomenon appears in the form of process, subject to strict rules of the algorithm, which placed the process of operation of the facility. Under the algorithmic model is the formalized description of the scenario subject specialist for the simulated process, the structure of which is comparable with the structure of the causal and temporal relationships between events of the process being modeled, together with all information necessary for its software implementation. To represent the structure of algorithmic models used algorithmic network. Normally, they were defined as loaded finite directed graph, the vertices which are mapped to operators and arcs are variables, bound by operators. The language of algorithmic networks has great features, the algorithms that it can display indifference the class of all random algorithms. In existing systems, automation modeling based on algorithmic nets, mainly used by operators working with real numbers. Although this reduces their ability, but enough for modeling a wide class of problems related to economy, environment, transport, technical processes. The task of modeling the execution of schedules and network diagrams is relevant and useful. There are many counting systems, network graphs, however, the monitoring process based analysis of gaps and terms of graphs, no analysis of prediction execution schedule or schedules. The library is designed to build similar predictive models. Specifying source data to obtain a set of projections from which to choose one and take it for a new plan.

  5. Named Entity Linking Algorithm

    Directory of Open Access Journals (Sweden)

    M. F. Panteleev

    2017-01-01

    Full Text Available In the tasks of processing text in natural language, Named Entity Linking (NEL represents the task to define and link some entity, which is found in the text, with some entity in the knowledge base (for example, Dbpedia. Currently, there is a diversity of approaches to solve this problem, but two main classes can be identified: graph-based approaches and machine learning-based ones. Graph and Machine Learning approaches-based algorithm is proposed accordingly to the stated assumptions about the interrelations of named entities in a sentence and in general.In the case of graph-based approaches, it is necessary to solve the problem of identifying an optimal set of the related entities according to some metric that characterizes the distance between these entities in a graph built on some knowledge base. Due to limitations in processing power, to solve this task directly is impossible. Therefore, its modification is proposed. Based on the algorithms of machine learning, an independent solution cannot be built due to small volumes of training datasets relevant to NEL task. However, their use can contribute to improving the quality of the algorithm. The adaptation of the Latent Dirichlet Allocation model is proposed in order to obtain a measure of the compatibility of attributes of various entities encountered in one context.The efficiency of the proposed algorithm was experimentally tested. A test dataset was independently generated. On its basis the performance of the model was compared using the proposed algorithm with the open source product DBpedia Spotlight, which solves the NEL problem.The mockup, based on the proposed algorithm, showed a low speed as compared to DBpedia Spotlight. However, the fact that it has shown higher accuracy, stipulates the prospects for work in this direction.The main directions of development were proposed in order to increase the accuracy of the system and its productivity.

  6. Bridging Weighted Rules and Graph Random Walks for Statistical Relational Models

    Directory of Open Access Journals (Sweden)

    Seyed Mehran Kazemi

    2018-02-01

    Full Text Available The aim of statistical relational learning is to learn statistical models from relational or graph-structured data. Three main statistical relational learning paradigms include weighted rule learning, random walks on graphs, and tensor factorization. These paradigms have been mostly developed and studied in isolation for many years, with few works attempting at understanding the relationship among them or combining them. In this article, we study the relationship between the path ranking algorithm (PRA, one of the most well-known relational learning methods in the graph random walk paradigm, and relational logistic regression (RLR, one of the recent developments in weighted rule learning. We provide a simple way to normalize relations and prove that relational logistic regression using normalized relations generalizes the path ranking algorithm. This result provides a better understanding of relational learning, especially for the weighted rule learning and graph random walk paradigms. It opens up the possibility of using the more flexible RLR rules within PRA models and even generalizing both by including normalized and unnormalized relations in the same model.

  7. Control Theoretical Expression of Quantum Systems And Lower Bound of Finite Horizon Quantum Algorithms

    OpenAIRE

    Yanagisawa, Masahiro

    2007-01-01

    We provide a control theoretical method for a computational lower bound of quantum algorithms based on quantum walks of a finite time horizon. It is shown that given a quantum network, there exists a control theoretical expression of the quantum system and the transition probability of the quantum walk is related to a norm of the associated transfer function.

  8. A Hybrid Approach to Processing Big Data Graphs on Memory-Restricted Systems

    KAUST Repository

    Harshvardhan,

    2015-05-01

    With the advent of big-data, processing large graphs quickly has become increasingly important. Most existing approaches either utilize in-memory processing techniques that can only process graphs that fit completely in RAM, or disk-based techniques that sacrifice performance. In this work, we propose a novel RAM-Disk hybrid approach to graph processing that can scale well from a single shared-memory node to large distributed-memory systems. It works by partitioning the graph into sub graphs that fit in RAM and uses a paging-like technique to load sub graphs. We show that without modifying the algorithms, this approach can scale from small memory-constrained systems (such as tablets) to large-scale distributed machines with 16, 000+ cores.

  9. SNAP: A General Purpose Network Analysis and Graph Mining Library.

    Science.gov (United States)

    Leskovec, Jure; Sosič, Rok

    2016-10-01

    Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. Here, we describe Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy to use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs where nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and meta-data on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic, they can be modified during the computation at low cost. SNAP is provided as an open source library in C++ as well as a module in Python. We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms.

  10. a Laser-Slam Algorithm for Indoor Mobile Mapping

    Science.gov (United States)

    Zhang, Wenjun; Zhang, Qiao; Sun, Kai; Guo, Sheng

    2016-06-01

    A novel Laser-SLAM algorithm is presented for real indoor environment mobile mapping. SLAM algorithm can be divided into two classes, Bayes filter-based and graph optimization-based. The former is often difficult to guarantee consistency and accuracy in largescale environment mapping because of the accumulative error during incremental mapping. Graph optimization-based SLAM method often assume predetermined landmarks, which is difficult to be got in unknown environment mapping. And there most likely has large difference between the optimize result and the real data, because the constraints are too few. This paper designed a kind of sub-map method, which could map more accurately without predetermined landmarks and avoid the already-drawn map impact on agent's location. The tree structure of sub-map can be indexed quickly and reduce the amount of memory consuming when mapping. The algorithm combined Bayes-based and graph optimization-based SLAM algorithm. It created virtual landmarks automatically by associating data of sub-maps for graph optimization. Then graph optimization guaranteed consistency and accuracy in large-scale environment mapping and improved the reasonability and reliability of the optimize results. Experimental results are presented with a laser sensor (UTM 30LX) in official buildings and shopping centres, which prove that the proposed algorithm can obtain 2D maps within 10cm precision in indoor environment range from several hundreds to 12000 square meter.

  11. Prediction by graph theoretic measures of structural effects in proteins arising from non-synonymous single nucleotide polymorphisms.

    Directory of Open Access Journals (Sweden)

    Tammy M K Cheng

    Full Text Available Recent analyses of human genome sequences have given rise to impressive advances in identifying non-synonymous single nucleotide polymorphisms (nsSNPs. By contrast, the annotation of nsSNPs and their links to diseases are progressing at a much slower pace. Many of the current approaches to analysing disease-associated nsSNPs use primarily sequence and evolutionary information, while structural information is relatively less exploited. In order to explore the potential of such information, we developed a structure-based approach, Bongo (Bonds ON Graph, to predict structural effects of nsSNPs. Bongo considers protein structures as residue-residue interaction networks and applies graph theoretical measures to identify the residues that are critical for maintaining structural stability by assessing the consequences on the interaction network of single point mutations. Our results show that Bongo is able to identify mutations that cause both local and global structural effects, with a remarkably low false positive rate. Application of the Bongo method to the prediction of 506 disease-associated nsSNPs resulted in a performance (positive predictive value, PPV, 78.5% similar to that of PolyPhen (PPV, 77.2% and PANTHER (PPV, 72.2%. As the Bongo method is solely structure-based, our results indicate that the structural changes resulting from nsSNPs are closely associated to their pathological consequences.

  12. Computing the Dilation of Edge-Augmented Graphs Embedded in Metric Spaces

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    2008-01-01

    Let G = (V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how...... to improve running time to O(n^3*log n) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G U {(u,v)} for every pair of distinct vertices u and v....

  13. Semantic content-based recommendations using semantic graphs.

    Science.gov (United States)

    Guo, Weisen; Kraines, Steven B

    2010-01-01

    Recommender systems (RSs) can be useful for suggesting items that might be of interest to specific users. Most existing content-based recommendation (CBR) systems are designed to recommend items based on text content, and the items in these systems are usually described with keywords. However, similarity evaluations based on keywords suffer from the ambiguity of natural languages. We present a semantic CBR method that uses Semantic Web technologies to recommend items that are more similar semantically with the items that the user prefers. We use semantic graphs to represent the items and we calculate the similarity scores for each pair of semantic graphs using an inverse graph frequency algorithm. The items having higher similarity scores to the items that are known to be preferred by the user are recommended.

  14. Mizan: A system for dynamic load balancing in large-scale graph processing

    KAUST Repository

    Khayyat, Zuhair

    2013-01-01

    Pregel [23] was recently introduced as a scalable graph mining system that can provide significant performance improvements over traditional MapReduce implementations. Existing implementations focus primarily on graph partitioning as a preprocessing step to balance computation across compute nodes. In this paper, we examine the runtime characteristics of a Pregel system. We show that graph partitioning alone is insufficient for minimizing end-to-end computation. Especially where data is very large or the runtime behavior of the algorithm is unknown, an adaptive approach is needed. To this end, we introduce Mizan, a Pregel system that achieves efficient load balancing to better adapt to changes in computing needs. Unlike known implementations of Pregel, Mizan does not assume any a priori knowledge of the structure of the graph or behavior of the algorithm. Instead, it monitors the runtime characteristics of the system. Mizan then performs efficient fine-grained vertex migration to balance computation and communication. We have fully implemented Mizan; using extensive evaluation we show that - especially for highly-dynamic workloads - Mizan provides up to 84% improvement over techniques leveraging static graph pre-partitioning. © 2013 ACM.

  15. Systematic benchmark of substructure search in molecular graphs - From Ullmann to VF2

    Directory of Open Access Journals (Sweden)

    Ehrlich Hans-Christian

    2012-07-01

    Full Text Available Abstract Background Searching for substructures in molecules belongs to the most elementary tasks in cheminformatics and is nowadays part of virtually every cheminformatics software. The underlying algorithms, used over several decades, are designed for the application to general graphs. Applied on molecular graphs, little effort has been spend on characterizing their performance. Therefore, it is not clear how current substructure search algorithms behave on such special graphs. One of the main reasons why such an evaluation was not performed in the past was the absence of appropriate data sets. Results In this paper, we present a systematic evaluation of Ullmann’s and the VF2 subgraph isomorphism algorithms on molecular data. The benchmark set consists of a collection of 1235 SMARTS substructure expressions and selected molecules from the ZINC database. The benchmark evaluates substructures search times for complete database scans as well as individual substructure-molecule pairs. In detail, we focus on the influence of substructure formulation and size, the impact of molecule size, and the ability of both algorithms to be used on multiple cores. Conclusions The results show a clear superiority of the VF2 algorithm in all test scenarios. In general, both algorithms solve most instances in less than one millisecond, which we consider to be acceptable. Still, in direct comparison, the VF2 is most often several folds faster than Ullmann’s algorithm. Additionally, Ullmann’s algorithm shows a surprising number of run time outliers.

  16. Geometric structure of chemistry-relevant graphs zigzags and central circuits

    CERN Document Server

    Deza, Michel-Marie; Shtogrin, Mikhail Ivanovitch

    2015-01-01

    The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.

  17. Some Results on the Intersection Graphs of Ideals of Rings

    International Nuclear Information System (INIS)

    Akbari, S.; Nikandish, R.; Nikmehr, M.J.

    2010-08-01

    Let R be a ring with unity and I(R)* be the set of all non-trivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct vertices I and J are adjacent if and only if I intersection J ≠ 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose intersection graphs of ideals are not connected. Also we determine all rings whose clique number of the intersection graphs of ideals are finite. Among other results, it is shown that for every ring, if the clique number of G(R) is finite, then the chromatic number is finite too and if R is a reduced ring both are equal. (author)

  18. Laplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems

    CERN Document Server

    Biyikoğu, Türker; Stadler, Peter F

    2007-01-01

    Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.

  19. Applying Graph Theory to Problems in Air Traffic Management

    Science.gov (United States)

    Farrahi, Amir H.; Goldberg, Alan T.; Bagasol, Leonard N.; Jung, Jaewoo

    2017-01-01

    Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

  20. Artistic image analysis using graph-based learning approaches.

    Science.gov (United States)

    Carneiro, Gustavo

    2013-08-01

    We introduce a new methodology for the problem of artistic image analysis, which among other tasks, involves the automatic identification of visual classes present in an art work. In this paper, we advocate the idea that artistic image analysis must explore a graph that captures the network of artistic influences by computing the similarities in terms of appearance and manual annotation. One of the novelties of our methodology is the proposed formulation that is a principled way of combining these two similarities in a single graph. Using this graph, we show that an efficient random walk algorithm based on an inverted label propagation formulation produces more accurate annotation and retrieval results compared with the following baseline algorithms: bag of visual words, label propagation, matrix completion, and structural learning. We also show that the proposed approach leads to a more efficient inference and training procedures. This experiment is run on a database containing 988 artistic images (with 49 visual classification problems divided into a multiclass problem with 27 classes and 48 binary problems), where we show the inference and training running times, and quantitative comparisons with respect to several retrieval and annotation performance measures.

  1. Evaluation of clustering algorithms for protein-protein interaction networks

    Directory of Open Access Journals (Sweden)

    van Helden Jacques

    2006-11-01

    Full Text Available Abstract Background Protein interactions are crucial components of all cellular processes. Recently, high-throughput methods have been developed to obtain a global description of the interactome (the whole network of protein interactions for a given organism. In 2002, the yeast interactome was estimated to contain up to 80,000 potential interactions. This estimate is based on the integration of data sets obtained by various methods (mass spectrometry, two-hybrid methods, genetic studies. High-throughput methods are known, however, to yield a non-negligible rate of false positives, and to miss a fraction of existing interactions. The interactome can be represented as a graph where nodes correspond with proteins and edges with pairwise interactions. In recent years clustering methods have been developed and applied in order to extract relevant modules from such graphs. These algorithms require the specification of parameters that may drastically affect the results. In this paper we present a comparative assessment of four algorithms: Markov Clustering (MCL, Restricted Neighborhood Search Clustering (RNSC, Super Paramagnetic Clustering (SPC, and Molecular Complex Detection (MCODE. Results A test graph was built on the basis of 220 complexes annotated in the MIPS database. To evaluate the robustness to false positives and false negatives, we derived 41 altered graphs by randomly removing edges from or adding edges to the test graph in various proportions. Each clustering algorithm was applied to these graphs with various parameter settings, and the clusters were compared with the annotated complexes. We analyzed the sensitivity of the algorithms to the parameters and determined their optimal parameter values. We also evaluated their robustness to alterations of the test graph. We then applied the four algorithms to six graphs obtained from high-throughput experiments and compared the resulting clusters with the annotated complexes. Conclusion This

  2. Significance evaluation in factor graphs

    DEFF Research Database (Denmark)

    Madsen, Tobias; Hobolth, Asger; Jensen, Jens Ledet

    2017-01-01

    in genomics and the multiple-testing issues accompanying them, accurate significance evaluation is of great importance. We here address the problem of evaluating statistical significance of observations from factor graph models. Results Two novel numerical approximations for evaluation of statistical...... significance are presented. First a method using importance sampling. Second a saddlepoint approximation based method. We develop algorithms to efficiently compute the approximations and compare them to naive sampling and the normal approximation. The individual merits of the methods are analysed both from....... Conclusions The applicability of saddlepoint approximation and importance sampling is demonstrated on known models in the factor graph framework. Using the two methods we can substantially improve computational cost without compromising accuracy. This contribution allows analyses of large datasets...

  3. Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

    KAUST Repository

    Abubeker, Jewahir Ali; Chikalov, Igor; Hussain, Shahid; Moshkov, Mikhail

    2011-01-01

    This paper is devoted to the consideration of an algorithm for sequential optimization of paths in directed graphs relative to di_erent cost functions. The considered algorithm is based on an extension of dynamic programming which allows

  4. An introduction to grids, graphs, and networks

    CERN Document Server

    Pozrikidis, C

    2014-01-01

    An Introduction to Grids, Graphs, and Networks aims to provide a concise introduction to graphs and networks at a level that is accessible to scientists, engineers, and students. In a practical approach, the book presents only the necessary theoretical concepts from mathematics and considers a variety of physical and conceptual configurations as prototypes or examples. The subject is timely, as the performance of networks is recognized as an important topic in the study of complex systems with applications in energy, material, and information grid transport (epitomized by the internet). The bo

  5. Quantum walks and search algorithms

    CERN Document Server

    Portugal, Renato

    2013-01-01

    This book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operater Analytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transforms Quantum walks on generic graphs, describing methods to calculate the limiting d...

  6. Graph-based Techniques for Topic Classification of Tweets in Spanish

    Directory of Open Access Journals (Sweden)

    Hector Cordobés

    2014-03-01

    Full Text Available Topic classification of texts is one of the most interesting challenges in Natural Language Processing (NLP. Topic classifiers commonly use a bag-of-words approach, in which the classifier uses (and is trained with selected terms from the input texts. In this work we present techniques based on graph similarity to classify short texts by topic. In our classifier we build graphs from the input texts, and then use properties of these graphs to classify them. We have tested the resulting algorithm by classifying Twitter messages in Spanish among a predefined set of topics, achieving more than 70% accuracy.

  7. Label-based routing for a family of scale-free, modular, planar and unclustered graphs

    International Nuclear Information System (INIS)

    Comellas, Francesc; Miralles, Alicia

    2011-01-01

    We give an optimal labeling and routing algorithm for a family of scale-free, modular and planar graphs with zero clustering. The relevant properties of this family match those of some networks associated with technological and biological systems with a low clustering, including some electronic circuits and protein networks. The existence of an efficient routing protocol for this graph model should help when designing communication algorithms in real networks and also in the understanding of their dynamic processes.

  8. A distributed query execution engine of big attributed graphs.

    Science.gov (United States)

    Batarfi, Omar; Elshawi, Radwa; Fayoumi, Ayman; Barnawi, Ahmed; Sakr, Sherif

    2016-01-01

    A graph is a popular data model that has become pervasively used for modeling structural relationships between objects. In practice, in many real-world graphs, the graph vertices and edges need to be associated with descriptive attributes. Such type of graphs are referred to as attributed graphs. G-SPARQL has been proposed as an expressive language, with a centralized execution engine, for querying attributed graphs. G-SPARQL supports various types of graph querying operations including reachability, pattern matching and shortest path where any G-SPARQL query may include value-based predicates on the descriptive information (attributes) of the graph edges/vertices in addition to the structural predicates. In general, a main limitation of centralized systems is that their vertical scalability is always restricted by the physical limits of computer systems. This article describes the design, implementation in addition to the performance evaluation of DG-SPARQL, a distributed, hybrid and adaptive parallel execution engine of G-SPARQL queries. In this engine, the topology of the graph is distributed over the main memory of the underlying nodes while the graph data are maintained in a relational store which is replicated on the disk of each of the underlying nodes. DG-SPARQL evaluates parts of the query plan via SQL queries which are pushed to the underlying relational stores while other parts of the query plan, as necessary, are evaluated via indexless memory-based graph traversal algorithms. Our experimental evaluation shows the efficiency and the scalability of DG-SPARQL on querying massive attributed graph datasets in addition to its ability to outperform the performance of Apache Giraph, a popular distributed graph processing system, by orders of magnitudes.

  9. Distributed graph coloring fundamentals and recent developments

    CERN Document Server

    Barenboim, Leonid

    2013-01-01

    The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible.A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging

  10. Generalized graph manifolds and their effective recognition

    International Nuclear Information System (INIS)

    Matveev, S V

    1998-01-01

    A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented

  11. SpectralNET – an application for spectral graph analysis and visualization

    Directory of Open Access Journals (Sweden)

    Schreiber Stuart L

    2005-10-01

    Full Text Available Abstract Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices and interactions (edges that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors. Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is

  12. Template Generation and Selection Algorithms

    NARCIS (Netherlands)

    Guo, Y.; Smit, Gerardus Johannes Maria; Broersma, Haitze J.; Heysters, P.M.; Badaway, W.; Ismail, Y.

    The availability of high-level design entry tooling is crucial for the viability of any reconfigurable SoC architecture. This paper presents a template generation method to extract functional equivalent structures, i.e. templates, from a control data flow graph. By inspecting the graph the algorithm

  13. Eigenfunction statistics on quantum graphs

    International Nuclear Information System (INIS)

    Gnutzmann, S.; Keating, J.P.; Piotet, F.

    2010-01-01

    We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.

  14. Methods of filtering the graph images of the functions

    Directory of Open Access Journals (Sweden)

    Олександр Григорович Бурса

    2017-06-01

    Full Text Available The theoretical aspects of cleaning raster images of scanned graphs of functions from digital, chromatic and luminance distortions by using computer graphics techniques have been considered. The basic types of distortions characteristic of graph images of functions have been stated. To suppress the distortion several methods, providing for high-quality of the resulting images and saving their topological features, were suggested. The paper describes the techniques developed and improved by the authors: the method of cleaning the image of distortions by means of iterative contrasting, based on the step-by-step increase in image contrast in the graph by 1%; the method of small entities distortion restoring, based on the thinning of the known matrix of contrast increase filter (the allowable dimensions of the nucleus dilution radius convolution matrix, which provide for the retention of the graph lines have been established; integration technique of the noise reduction method by means of contrasting and distortion restoring method of small entities with known σ-filter. Each method in the complex has been theoretically substantiated. The developed methods involve treatment of graph images as the entire image (global processing and its fragments (local processing. The metrics assessing the quality of the resulting image with the global and local processing have been chosen, the substantiation of the choice as well as the formulas have been given. The proposed complex methods of cleaning the graphs images of functions from grayscale image distortions is adaptive to the form of an image carrier, the distortion level in the image and its distribution. The presented results of testing the developed complex of methods for a representative sample of images confirm its effectiveness

  15. Exclusivity structures and graph representatives of local complementation orbits

    Science.gov (United States)

    Cabello, Adán; Parker, Matthew G.; Scarpa, Giannicola; Severini, Simone

    2013-07-01

    We describe a construction that maps any connected graph G on three or more vertices into a larger graph, H(G), whose independence number is strictly smaller than its Lovász number which is equal to its fractional packing number. The vertices of H(G) represent all possible events consistent with the stabilizer group of the graph state associated with G, and exclusive events are adjacent. Mathematically, the graph H(G) corresponds to the orbit of G under local complementation. Physically, the construction translates into graph-theoretic terms the connection between a graph state and a Bell inequality maximally violated by quantum mechanics. In the context of zero-error information theory, the construction suggests a protocol achieving the maximum rate of entanglement-assisted capacity, a quantum mechanical analogue of the Shannon capacity, for each H(G). The violation of the Bell inequality is expressed by the one-shot version of this capacity being strictly larger than the independence number. Finally, given the correspondence between graphs and exclusivity structures, we are able to compute the independence number for certain infinite families of graphs with the use of quantum non-locality, therefore highlighting an application of quantum theory in the proof of a purely combinatorial statement.

  16. Better bounds for incremental frequency allocation in bipartite graphs

    Czech Academy of Sciences Publication Activity Database

    Chrobak, M.; Jeż, Łukasz; Sgall, J.

    2013-01-01

    Roč. 514, 25 November (2013), s. 75-83 ISSN 0304-3975 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : online algorithms * frequency allocation * graph algorithms Subject RIV: BA - General Mathematics Impact factor: 0.516, year: 2013 http://www.sciencedirect.com/science/article/pii/S0304397512004781

  17. Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

    Science.gov (United States)

    Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.; Cano, Jennifer; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei

    2018-01-01

    The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

  18. A linear time algorithm for minimum fill-in and treewidth for distance heredity graphs

    NARCIS (Netherlands)

    Broersma, Haitze J.; Dahlhaus, E.; Kloks, A.J.J.; Kloks, T.

    2000-01-01

    A graph is distance hereditary if it preserves distances in all its connected induced subgraphs. The MINIMUM FILL-IN problem is the problem of finding a chordal supergraph with the smallest possible number of edges. The TREEWIDTH problem is the problem of finding a chordal embedding of the graph

  19. CiSE: a circular spring embedder layout algorithm.

    Science.gov (United States)

    Dogrusoz, Ugur; Belviranli, Mehmet E; Dilek, Alptug

    2013-06-01

    We present a new algorithm for automatic layout of clustered graphs using a circular style. The algorithm tries to determine optimal location and orientation of individual clusters intrinsically within a modified spring embedder. Heuristics such as reversal of the order of nodes in a cluster and swap of neighboring node pairs in the same cluster are employed intermittently to further relax the spring embedder system, resulting in reduced inter-cluster edge crossings. Unlike other algorithms generating circular drawings, our algorithm does not require the quotient graph to be acyclic, nor does it sacrifice the edge crossing number of individual clusters to improve respective positioning of the clusters. Moreover, it reduces the total area required by a cluster by using the space inside the associated circle. Experimental results show that the execution time and quality of the produced drawings with respect to commonly accepted layout criteria are quite satisfactory, surpassing previous algorithms. The algorithm has also been successfully implemented and made publicly available as part of a compound and clustered graph editing and layout tool named CHISIO.

  20. Graph-theoretic measures of multivariate association and prediction

    International Nuclear Information System (INIS)

    Friedman, J.H.; Rafsky, L.C.

    1983-01-01

    Interpoint-distance-based graphs can be used to define measures of association that extend Kendall's notion of a generalized correlation coefficient. The authors present particular statistics that provide distribution-free tests of independence sensitive to alternatives involving non-monotonic relationships. Moreover, since ordering plays no essential role, the ideas that fully applicable in a multivariate setting. The authors also define an asymmetric coefficient measuring the extent to which (a vector) X can be used to make single-valued predictions of (a vector) Y. The authors discuss various techniques for proving that such statistics are asymptotically normal. As an example of the effectiveness of their approach, the authors present an application to the examination of residuals from multiple regression. 18 references, 2 figures, 1 table

  1. Mining the inner structure of the Web graph

    International Nuclear Information System (INIS)

    Donato, Debora; Leonardi, Stefano; Millozzi, Stefano; Tsaparas, Panayiotis

    2008-01-01

    Despite being the sum of decentralized and uncoordinated efforts by heterogeneous groups and individuals, the World Wide Web exhibits a well-defined structure, characterized by several interesting properties. This structure was clearly revealed by Broder et al (2000 Graph structure in the web Comput. Netw. 33 309) who presented the evocative bow-tie picture of the Web. Although, the bow-tie structure is a relatively clear abstraction of the macroscopic picture of the Web, it is quite uninformative with respect to the finer details of the Web graph. In this paper, we mine the inner structure of the Web graph. We present a series of measurements on the Web, which offer a better understanding of the individual components of the bow-tie. In the process, we develop algorithmic techniques for performing these measurements. We discover that the scale-free properties permeate all the components of the bow-tie which exhibit the same macroscopic properties as the Web graph itself. However, close inspection reveals that their inner structure is quite distinct. We show that the Web graph does not exhibit self similarity within its components, and we propose a possible alternative picture for the Web graph, as it emerges from our experiments

  2. Algorithmic approach to diagram techniques

    International Nuclear Information System (INIS)

    Ponticopoulos, L.

    1980-10-01

    An algorithmic approach to diagram techniques of elementary particles is proposed. The definition and axiomatics of the theory of algorithms are presented, followed by the list of instructions of an algorithm formalizing the construction of graphs and the assignment of mathematical objects to them. (T.A.)

  3. BFL: a node and edge betweenness based fast layout algorithm for large scale networks

    Science.gov (United States)

    Hashimoto, Tatsunori B; Nagasaki, Masao; Kojima, Kaname; Miyano, Satoru

    2009-01-01

    Background Network visualization would serve as a useful first step for analysis. However, current graph layout algorithms for biological pathways are insensitive to biologically important information, e.g. subcellular localization, biological node and graph attributes, or/and not available for large scale networks, e.g. more than 10000 elements. Results To overcome these problems, we propose the use of a biologically important graph metric, betweenness, a measure of network flow. This metric is highly correlated with many biological phenomena such as lethality and clusters. We devise a new fast parallel algorithm calculating betweenness to minimize the preprocessing cost. Using this metric, we also invent a node and edge betweenness based fast layout algorithm (BFL). BFL places the high-betweenness nodes to optimal positions and allows the low-betweenness nodes to reach suboptimal positions. Furthermore, BFL reduces the runtime by combining a sequential insertion algorim with betweenness. For a graph with n nodes, this approach reduces the expected runtime of the algorithm to O(n2) when considering edge crossings, and to O(n log n) when considering only density and edge lengths. Conclusion Our BFL algorithm is compared against fast graph layout algorithms and approaches requiring intensive optimizations. For gene networks, we show that our algorithm is faster than all layout algorithms tested while providing readability on par with intensive optimization algorithms. We achieve a 1.4 second runtime for a graph with 4000 nodes and 12000 edges on a standard desktop computer. PMID:19146673

  4. Attributed relational graphs for cell nucleus segmentation in fluorescence microscopy images.

    Science.gov (United States)

    Arslan, Salim; Ersahin, Tulin; Cetin-Atalay, Rengul; Gunduz-Demir, Cigdem

    2013-06-01

    More rapid and accurate high-throughput screening in molecular cellular biology research has become possible with the development of automated microscopy imaging, for which cell nucleus segmentation commonly constitutes the core step. Although several promising methods exist for segmenting the nuclei of monolayer isolated and less-confluent cells, it still remains an open problem to segment the nuclei of more-confluent cells, which tend to grow in overlayers. To address this problem, we propose a new model-based nucleus segmentation algorithm. This algorithm models how a human locates a nucleus by identifying the nucleus boundaries and piecing them together. In this algorithm, we define four types of primitives to represent nucleus boundaries at different orientations and construct an attributed relational graph on the primitives to represent their spatial relations. Then, we reduce the nucleus identification problem to finding predefined structural patterns in the constructed graph and also use the primitives in region growing to delineate the nucleus borders. Working with fluorescence microscopy images, our experiments demonstrate that the proposed algorithm identifies nuclei better than previous nucleus segmentation algorithms.

  5. Diffusion-based recommendation with trust relations on tripartite graphs

    Science.gov (United States)

    Wang, Ximeng; Liu, Yun; Zhang, Guangquan; Xiong, Fei; Lu, Jie

    2017-08-01

    The diffusion-based recommendation approach is a vital branch in recommender systems, which successfully applies physical dynamics to make recommendations for users on bipartite or tripartite graphs. Trust links indicate users’ social relations and can provide the benefit of reducing data sparsity. However, traditional diffusion-based algorithms only consider rating links when making recommendations. In this paper, the complementarity of users’ implicit and explicit trust is exploited, and a novel resource-allocation strategy is proposed, which integrates these two kinds of trust relations on tripartite graphs. Through empirical studies on three benchmark datasets, our proposed method obtains better performance than most of the benchmark algorithms in terms of accuracy, diversity and novelty. According to the experimental results, our method is an effective and reasonable way to integrate additional features into the diffusion-based recommendation approach.

  6. Object recognition in images via a factor graph model

    Science.gov (United States)

    He, Yong; Wang, Long; Wu, Zhaolin; Zhang, Haisu

    2018-04-01

    Object recognition in images suffered from huge search space and uncertain object profile. Recently, the Bag-of- Words methods are utilized to solve these problems, especially the 2-dimension CRF(Conditional Random Field) model. In this paper we suggest the method based on a general and flexible fact graph model, which can catch the long-range correlation in Bag-of-Words by constructing a network learning framework contrasted from lattice in CRF. Furthermore, we explore a parameter learning algorithm based on the gradient descent and Loopy Sum-Product algorithms for the factor graph model. Experimental results on Graz 02 dataset show that, the recognition performance of our method in precision and recall is better than a state-of-art method and the original CRF model, demonstrating the effectiveness of the proposed method.

  7. Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices.

    Science.gov (United States)

    Dehmer, Matthias; Emmert-Streib, Frank; Shi, Yongtang; Stefu, Monica; Tripathi, Shailesh

    2015-01-01

    In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164-168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work.

  8. A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.

    Science.gov (United States)

    Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang

    2016-04-01

    Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.

  9. On the reachability and observability of path and cycle graphs

    OpenAIRE

    Parlangeli, Gianfranco; Notarstefano, Giuseppe

    2011-01-01

    In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph...

  10. Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs

    Energy Technology Data Exchange (ETDEWEB)

    Mota, A; Knap, J; Ortiz, M

    2006-10-18

    An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.

  11. Multithreaded Asynchronous Graph Traversal for In-Memory and Semi-External Memory

    KAUST Repository

    Pearce, Roger

    2010-11-01

    Processing large graphs is becoming increasingly important for many domains such as social networks, bioinformatics, etc. Unfortunately, many algorithms and implementations do not scale with increasing graph sizes. As a result, researchers have attempted to meet the growing data demands using parallel and external memory techniques. We present a novel asynchronous approach to compute Breadth-First-Search (BFS), Single-Source-Shortest-Paths, and Connected Components for large graphs in shared memory. Our highly parallel asynchronous approach hides data latency due to both poor locality and delays in the underlying graph data storage. We present an experimental study applying our technique to both In-Memory and Semi-External Memory graphs utilizing multi-core processors and solid-state memory devices. Our experiments using synthetic and real-world datasets show that our asynchronous approach is able to overcome data latencies and provide significant speedup over alternative approaches. For example, on billion vertex graphs our asynchronous BFS scales up to 14x on 16-cores. © 2010 IEEE.

  12. GCPSO in cooperation with graph theory to distribution network reconfiguration for energy saving

    International Nuclear Information System (INIS)

    Assadian, Mehdi; Farsangi, Malihe M.; Nezamabadi-pour, Hossein

    2010-01-01

    Network reconfiguration for loss reduction in distribution system is an important way to save energy. This paper investigates the ability of guaranteed convergence particle swarm optimization (GCPSO) and particle swarm optimization (PSO) in cooperation with graph theory for network reconfiguration to reduce the power loss and enhancement of voltage profile of distribution systems. Numerical results of three distribution systems are presented which illustrate the feasibility of the proposed method by GCPSO and PSO using the graph theory. To validate the obtained results, genetic algorithm (GA) using graph theory is also applied and is compared with the proposed GCPSO and PSO using graph theory.

  13. Efficient growth of complex graph states via imperfect path erasure

    International Nuclear Information System (INIS)

    Campbell, Earl T; Fitzsimons, Joseph; Benjamin, Simon C; Kok, Pieter

    2007-01-01

    Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect entanglement into an extended graph state formalism. The subsequent growth of the improper graph state can be guided, through a series of strategic decisions, in such a way as to bound the growth of the error and eventually yield a high-fidelity graph state. As an implementation of these techniques, we develop an analytic model for atom (or atom-like) qubits in mismatched cavities, under the double-heralding entanglement procedure of Barrett and Kok (2005 Phys. Rev. A 71 060310). Compared to straightforward post-selection techniques our protocol offers a dramatic improvement in growing complex high-fidelity graph states

  14. Voice-Centric LTE Femtocells and Improper Graph Colorings

    DEFF Research Database (Denmark)

    Garcia, Luis Guilherme Uzeda; Pedersen, Klaus; Mogensen, Preben

    2012-01-01

    . The investigation revolves around the sensible definition of the underlying graph, i.e. the network model, rather than focusing on the coloring algorithms and their properties. Ultimately, we posit that improper online graph-coloring suffices and is actually preferable. In short, settling for less......This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring......-than-optimal configurations avoids uncontrolled service interruptions. Such disruptions tend to raise understandable concerns when it comes to fully autonomous selection of operational CCs. Our results dispel such concerns by showing that conservative methods can achieve most of the benefits of unrestricted off-line coloring...

  15. Attributed community mining using joint general non-negative matrix factorization with graph Laplacian

    Science.gov (United States)

    Chen, Zigang; Li, Lixiang; Peng, Haipeng; Liu, Yuhong; Yang, Yixian

    2018-04-01

    Community mining for complex social networks with link and attribute information plays an important role according to different application needs. In this paper, based on our proposed general non-negative matrix factorization (GNMF) algorithm without dimension matching constraints in our previous work, we propose the joint GNMF with graph Laplacian (LJGNMF) to implement community mining of complex social networks with link and attribute information according to different application needs. Theoretical derivation result shows that the proposed LJGNMF is fully compatible with previous methods of integrating traditional NMF and symmetric NMF. In addition, experimental results show that the proposed LJGNMF can meet the needs of different community minings by adjusting its parameters, and the effect is better than traditional NMF in the community vertices attributes entropy.

  16. Segmentation of Synchrotron Radiation micro-Computed Tomography Images using Energy Minimization via Graph Cuts

    International Nuclear Information System (INIS)

    Meneses, Anderson A.M.; Giusti, Alessandro; Almeida, André P. de; Nogueira, Liebert; Braz, Delson; Almeida, Carlos E. de; Barroso, Regina C.

    2012-01-01

    The research on applications of segmentation algorithms to Synchrotron Radiation X-Ray micro-Computed Tomography (SR-μCT) is an open problem, due to the interesting and well-known characteristics of SR images, such as the phase contrast effect. The Energy Minimization via Graph Cuts (EMvGC) algorithm represents state-of-art segmentation algorithm, presenting an enormous potential of application in SR-μCT imaging. We describe the application of the algorithm EMvGC with swap move for the segmentation of bone images acquired at the ELETTRA Laboratory (Trieste, Italy). - Highlights: ► Microstructures of Wistar rats' ribs are investigated with Synchrotron Radiation μCT imaging. ► The present work is part of a research on the effects of radiotherapy on the thoracic region. ► Application of the Energy Minimization via Graph Cuts algorithm for segmentation is described.

  17. Nonschematic drawing recognition: a new approach based on attributed graph grammar with flexible embedding

    Science.gov (United States)

    Lee, Kyu J.; Kunii, T. L.; Noma, T.

    1993-01-01

    In this paper, we propose a syntactic pattern recognition method for non-schematic drawings, based on a new attributed graph grammar with flexible embedding. In our graph grammar, the embedding rule permits the nodes of a guest graph to be arbitrarily connected with the nodes of a host graph. The ambiguity caused by this flexible embedding is controlled with the evaluation of synthesized attributes and the check of context sensitivity. To integrate parsing with the synthesized attribute evaluation and the context sensitivity check, we also develop a bottom up parsing algorithm.

  18. Intrinsic functional brain architecture derived from graph theoretical analysis in the human fetus.

    Directory of Open Access Journals (Sweden)

    Moriah E Thomason

    Full Text Available The human brain undergoes dramatic maturational changes during late stages of fetal and early postnatal life. The importance of this period to the establishment of healthy neural connectivity is apparent in the high incidence of neural injury in preterm infants, in whom untimely exposure to ex-uterine factors interrupts neural connectivity. Though the relevance of this period to human neuroscience is apparent, little is known about functional neural networks in human fetal life. Here, we apply graph theoretical analysis to examine human fetal brain connectivity. Utilizing resting state functional magnetic resonance imaging (fMRI data from 33 healthy human fetuses, 19 to 39 weeks gestational age (GA, our analyses reveal that the human fetal brain has modular organization and modules overlap functional systems observed postnatally. Age-related differences between younger (GA <31 weeks and older (GA≥31 weeks fetuses demonstrate that brain modularity decreases, and connectivity of the posterior cingulate to other brain networks becomes more negative, with advancing GA. By mimicking functional principles observed postnatally, these results support early emerging capacity for information processing in the human fetal brain. Current technical limitations, as well as the potential for fetal fMRI to one day produce major discoveries about fetal origins or antecedents of neural injury or disease are discussed.

  19. A librarian's guide to graphs, data and the semantic web

    CERN Document Server

    Powell, James

    2015-01-01

    Graphs are about connections, and are an important part of our connected and data-driven world. A Librarian's Guide to Graphs, Data and the Semantic Web is geared toward library and information science professionals, including librarians, software developers and information systems architects who want to understand the fundamentals of graph theory, how it is used to represent and explore data, and how it relates to the semantic web. This title provides a firm grounding in the field at a level suitable for a broad audience, with an emphasis on open source solutions and what problems these tools solve at a conceptual level, with minimal emphasis on algorithms or mathematics. The text will also be of special interest to data science librarians and data professionals, since it introduces many graph theory concepts by exploring data-driven networks from various scientific disciplines. The first two chapters consider graphs in theory and the science of networks, before the following chapters cover networks in vario...

  20. Using a High-Dimensional Graph of Semantic Space to Model Relationships among Words

    Directory of Open Access Journals (Sweden)

    Alice F Jackson

    2014-05-01

    Full Text Available The GOLD model (Graph Of Language Distribution is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA. The superior performance of the GOLD models (big and small suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition.

  1. Using a high-dimensional graph of semantic space to model relationships among words.

    Science.gov (United States)

    Jackson, Alice F; Bolger, Donald J

    2014-01-01

    The GOLD model (Graph Of Language Distribution) is a network model constructed based on co-occurrence in a large corpus of natural language that may be used to explore what information may be present in a graph-structured model of language, and what information may be extracted through theoretically-driven algorithms as well as standard graph analysis methods. The present study will employ GOLD to examine two types of relationship between words: semantic similarity and associative relatedness. Semantic similarity refers to the degree of overlap in meaning between words, while associative relatedness refers to the degree to which two words occur in the same schematic context. It is expected that a graph structured model of language constructed based on co-occurrence should easily capture associative relatedness, because this type of relationship is thought to be present directly in lexical co-occurrence. However, it is hypothesized that semantic similarity may be extracted from the intersection of the set of first-order connections, because two words that are semantically similar may occupy similar thematic or syntactic roles across contexts and thus would co-occur lexically with the same set of nodes. Two versions the GOLD model that differed in terms of the co-occurence window, bigGOLD at the paragraph level and smallGOLD at the adjacent word level, were directly compared to the performance of a well-established distributional model, Latent Semantic Analysis (LSA). The superior performance of the GOLD models (big and small) suggest that a single acquisition and storage mechanism, namely co-occurrence, can account for associative and conceptual relationships between words and is more psychologically plausible than models using singular value decomposition (SVD).

  2. Image interpolation via graph-based Bayesian label propagation.

    Science.gov (United States)

    Xianming Liu; Debin Zhao; Jiantao Zhou; Wen Gao; Huifang Sun

    2014-03-01

    In this paper, we propose a novel image interpolation algorithm via graph-based Bayesian label propagation. The basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices, then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones. This process can be posed as a Bayesian inference, in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation. Specially, our algorithm first constructs a set of local interpolation models, which predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of the available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Moreover, a graph-Laplacian-based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the global loss of the locally linear regression, square error of prediction bias on the available LR samples, and the manifold regularization term. It can be solved with a closed-form solution as a convex optimization problem. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art image interpolation algorithms.

  3. Dynamic airspace configuration algorithms for next generation air transportation system

    Science.gov (United States)

    Wei, Jian

    The National Airspace System (NAS) is under great pressure to safely and efficiently handle the record-high air traffic volume nowadays, and will face even greater challenge to keep pace with the steady increase of future air travel demand, since the air travel demand is projected to increase to two to three times the current level by 2025. The inefficiency of traffic flow management initiatives causes severe airspace congestion and frequent flight delays, which cost billions of economic losses every year. To address the increasingly severe airspace congestion and delays, the Next Generation Air Transportation System (NextGen) is proposed to transform the current static and rigid radar based system to a dynamic and flexible satellite based system. New operational concepts such as Dynamic Airspace Configuration (DAC) have been under development to allow more flexibility required to mitigate the demand-capacity imbalances in order to increase the throughput of the entire NAS. In this dissertation, we address the DAC problem in the en route and terminal airspace under the framework of NextGen. We develop a series of algorithms to facilitate the implementation of innovative concepts relevant with DAC in both the en route and terminal airspace. We also develop a performance evaluation framework for comprehensive benefit analyses on different aspects of future sector design algorithms. First, we complete a graph based sectorization algorithm for DAC in the en route airspace, which models the underlying air route network with a weighted graph, converts the sectorization problem into the graph partition problem, partitions the weighted graph with an iterative spectral bipartition method, and constructs the sectors from the partitioned graph. The algorithm uses a graph model to accurately capture the complex traffic patterns of the real flights, and generates sectors with high efficiency while evenly distributing the workload among the generated sectors. We further improve

  4. Balanced Bipartite Graph Based Register Allocation for Network Processors in Mobile and Wireless Networks

    Directory of Open Access Journals (Sweden)

    Feilong Tang

    2010-01-01

    Full Text Available Mobile and wireless networks are the integrant infrastructure of mobile and pervasive computing that aims at providing transparent and preferred information and services for people anytime anywhere. In such environments, end-to-end network bandwidth is crucial to improve user's transparent experience when providing on-demand services such as mobile video playing. As a result, powerful computing power is required for networked nodes, especially for routers. General-purpose processors cannot meet such requirements due to their limited processing ability, and poor programmability and scalability. Intel's network processor IXP is specially designed for fast packet processing to achieve a broad bandwidth. IXP provides a large number of registers to reduce the number of memory accesses. Registers in an IXP are physically partitioned as two banks so that two source operands in an instruction have to come from the two banks respectively, which makes the IXP register allocation tricky and different from conventional ones. In this paper, we investigate an approach for efficiently generating balanced bipartite graph and register allocation algorithms for the dual-bank register allocation in IXPs. The paper presents a graph uniform 2-way partition algorithm (FPT, which provides an optimal solution to the graph partition, and a heuristic algorithm for generating balanced bipartite graph. Finally, we design a framework for IXP register allocation. Experimental results demonstrate the framework and the algorithms are efficient in register allocation for IXP network processors.

  5. Graph Aggregation

    NARCIS (Netherlands)

    Endriss, U.; Grandi, U.

    Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference

  6. Impact of Locality on Location Aware Unit Disk Graphs

    Directory of Open Access Journals (Sweden)

    Evangelos Kranakis

    2008-09-01

    Full Text Available Due to their importance for studies oi wireless networks, recent years have seen a surge of activity on the design of local algorithms for the solution of a variety of network tasks. We study the behaviour of algorithms with very low localities. Despite of this restriction we propose local constant ratio approximation algorithms for solving minimum dominating and connected dominating set, maximum independent set and minimum vertex cover in location aware Unit Disk Graphs. We also prove the first ever lower bounds for local algorithms for these problems with a given locality in the location aware setting.

  7. Bayesian analysis for exponential random graph models using the adaptive exchange sampler

    KAUST Repository

    Jin, Ick Hoon

    2013-01-01

    Exponential random graph models have been widely used in social network analysis. However, these models are extremely difficult to handle from a statistical viewpoint, because of the existence of intractable normalizing constants. In this paper, we consider a fully Bayesian analysis for exponential random graph models using the adaptive exchange sampler, which solves the issue of intractable normalizing constants encountered in Markov chain Monte Carlo (MCMC) simulations. The adaptive exchange sampler can be viewed as a MCMC extension of the exchange algorithm, and it generates auxiliary networks via an importance sampling procedure from an auxiliary Markov chain running in parallel. The convergence of this algorithm is established under mild conditions. The adaptive exchange sampler is illustrated using a few social networks, including the Florentine business network, molecule synthetic network, and dolphins network. The results indicate that the adaptive exchange algorithm can produce more accurate estimates than approximate exchange algorithms, while maintaining the same computational efficiency.

  8. iBGP: A Bipartite Graph Propagation Approach for Mobile Advertising Fraud Detection

    Directory of Open Access Journals (Sweden)

    Jinlong Hu

    2017-01-01

    Full Text Available Online mobile advertising plays a vital financial role in supporting free mobile apps, but detecting malicious apps publishers who generate fraudulent actions on the advertisements hosted on their apps is difficult, since fraudulent traffic often mimics behaviors of legitimate users and evolves rapidly. In this paper, we propose a novel bipartite graph-based propagation approach, iBGP, for mobile apps advertising fraud detection in large advertising system. We exploit the characteristics of mobile advertising user’s behavior and identify two persistent patterns: power law distribution and pertinence and propose an automatic initial score learning algorithm to formulate both concepts to learn the initial scores of non-seed nodes. We propose a weighted graph propagation algorithm to propagate the scores of all nodes in the user-app bipartite graphs until convergence. To extend our approach for large-scale settings, we decompose the objective function of the initial score learning model into separate one-dimensional problems and parallelize the whole approach on an Apache Spark cluster. iBGP was applied on a large synthetic dataset and a large real-world mobile advertising dataset; experiment results demonstrate that iBGP significantly outperforms other popular graph-based propagation methods.

  9. Segmentation of Synchrotron Radiation micro-Computed Tomography Images using Energy Minimization via Graph Cuts

    Energy Technology Data Exchange (ETDEWEB)

    Meneses, Anderson A.M. [Federal University of Western Para (Brazil); Physics Institute, Rio de Janeiro State University (Brazil); Giusti, Alessandro [IDSIA (Dalle Molle Institute for Artificial Intelligence), University of Lugano (Switzerland); Almeida, Andre P. de, E-mail: apalmeid@gmail.com [Physics Institute, Rio de Janeiro State University (Brazil); Nuclear Engineering Program, Federal University of Rio de Janeiro (Brazil); Nogueira, Liebert; Braz, Delson [Nuclear Engineering Program, Federal University of Rio de Janeiro (Brazil); Almeida, Carlos E. de [Radiological Sciences Laboratory, Rio de Janeiro State University (Brazil); Barroso, Regina C. [Physics Institute, Rio de Janeiro State University (Brazil)

    2012-07-15

    The research on applications of segmentation algorithms to Synchrotron Radiation X-Ray micro-Computed Tomography (SR-{mu}CT) is an open problem, due to the interesting and well-known characteristics of SR images, such as the phase contrast effect. The Energy Minimization via Graph Cuts (EMvGC) algorithm represents state-of-art segmentation algorithm, presenting an enormous potential of application in SR-{mu}CT imaging. We describe the application of the algorithm EMvGC with swap move for the segmentation of bone images acquired at the ELETTRA Laboratory (Trieste, Italy). - Highlights: Black-Right-Pointing-Pointer Microstructures of Wistar rats' ribs are investigated with Synchrotron Radiation {mu}CT imaging. Black-Right-Pointing-Pointer The present work is part of a research on the effects of radiotherapy on the thoracic region. Black-Right-Pointing-Pointer Application of the Energy Minimization via Graph Cuts algorithm for segmentation is described.

  10. Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

    Science.gov (United States)

    Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

    2017-12-01

    We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory—such as Hall's marriage problem—are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

  11. Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings.

    Science.gov (United States)

    Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

    2017-12-15

    We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

  12. Méthodes de graphe pour la segmentation d'images et le suivi d'objets dynamiques

    OpenAIRE

    Wang , Xiaofang

    2015-01-01

    Image segmentation is a fundamental problem in computer vision. In particular, unsupervised image segmentation is an important component in many high-level algorithms and practical vision systems. In this dissertation, we propose three methods that approach image segmentation from different angles of graph based methods and are proved powerful to address these problems. Our first method develops an original graph construction method. We also analyze different types of graph construction metho...

  13. The structured ancestral selection graph and the many-demes limit.

    Science.gov (United States)

    Slade, Paul F; Wakeley, John

    2005-02-01

    We show that the unstructured ancestral selection graph applies to part of the history of a sample from a population structured by restricted migration among subpopulations, or demes. The result holds in the limit as the number of demes tends to infinity with proportionately weak selection, and we have also made the assumptions of island-type migration and that demes are equivalent in size. After an instantaneous sample-size adjustment, this structured ancestral selection graph converges to an unstructured ancestral selection graph with a mutation parameter that depends inversely on the migration rate. In contrast, the selection parameter for the population is independent of the migration rate and is identical to the selection parameter in an unstructured population. We show analytically that estimators of the migration rate, based on pairwise sequence differences, derived under the assumption of neutrality should perform equally well in the presence of weak selection. We also modify an algorithm for simulating genealogies conditional on the frequencies of two selected alleles in a sample. This permits efficient simulation of stronger selection than was previously possible. Using this new algorithm, we simulate gene genealogies under the many-demes ancestral selection graph and identify some situations in which migration has a strong effect on the time to the most recent common ancestor of the sample. We find that a similar effect also increases the sensitivity of the genealogy to selection.

  14. Efficient Sampling of the Structure of Crypto Generators' State Transition Graphs

    Science.gov (United States)

    Keller, Jörg

    Cryptographic generators, e.g. stream cipher generators like the A5/1 used in GSM networks or pseudo-random number generators, are widely used in cryptographic network protocols. Basically, they are finite state machines with deterministic transition functions. Their state transition graphs typically cannot be analyzed analytically, nor can they be explored completely because of their size which typically is at least n = 264. Yet, their structure, i.e. number and sizes of weakly connected components, is of interest because a structure deviating significantly from expected values for random graphs may form a distinguishing attack that indicates a weakness or backdoor. By sampling, one randomly chooses k nodes, derives their distribution onto connected components by graph exploration, and extrapolates these results to the complete graph. In known algorithms, the computational cost to determine the component for one randomly chosen node is up to O(√n), which severely restricts the sample size k. We present an algorithm where the computational cost to find the connected component for one randomly chosen node is O(1), so that a much larger sample size k can be analyzed in a given time. We report on the performance of a prototype implementation, and about preliminary analysis for several generators.

  15. Optimal improvement of graphs related to nuclear safeguards problems

    International Nuclear Information System (INIS)

    Jacobsen, S.E.

    1977-08-01

    This report develops the methodology for optimally improving graphs related to nuclear safeguards issues. In particular, given a fixed number of dollars, the report provides a method for optimally allocating such dollars over the arcs of a weighted graph (the weights vary as a function of dollars spent on arcs) so as to improve the system effectiveness measure which is the shortest of all shortest paths to several targets. Arc weights can be either clock times or detection probabilities and the algorithm does not explicitly consider all paths to the targets

  16. Learning molecular energies using localized graph kernels

    Science.gov (United States)

    Ferré, Grégoire; Haut, Terry; Barros, Kipton

    2017-03-01

    Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. We benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

  17. Semantic Health Knowledge Graph: Semantic Integration of Heterogeneous Medical Knowledge and Services

    Directory of Open Access Journals (Sweden)

    Longxiang Shi

    2017-01-01

    Full Text Available With the explosion of healthcare information, there has been a tremendous amount of heterogeneous textual medical knowledge (TMK, which plays an essential role in healthcare information systems. Existing works for integrating and utilizing the TMK mainly focus on straightforward connections establishment and pay less attention to make computers interpret and retrieve knowledge correctly and quickly. In this paper, we explore a novel model to organize and integrate the TMK into conceptual graphs. We then employ a framework to automatically retrieve knowledge in knowledge graphs with a high precision. In order to perform reasonable inference on knowledge graphs, we propose a contextual inference pruning algorithm to achieve efficient chain inference. Our algorithm achieves a better inference result with precision and recall of 92% and 96%, respectively, which can avoid most of the meaningless inferences. In addition, we implement two prototypes and provide services, and the results show our approach is practical and effective.

  18. Solving Problem of Graph Isomorphism by Membrane-Quantum Hybrid Model

    Directory of Open Access Journals (Sweden)

    Artiom Alhazov

    2015-10-01

    Full Text Available This work presents the application of new parallelization methods based on membrane-quantum hybrid computing to graph isomorphism problem solving. Applied membrane-quantum hybrid computational model was developed by authors. Massive parallelism of unconventional computing is used to implement classic brute force algorithm efficiently. This approach does not suppose any restrictions of considered graphs types. The estimated performance of the model is less then quadratic that makes a very good result for the problem of \\textbf{NP} complexity.

  19. Proxy Graph: Visual Quality Metrics of Big Graph Sampling.

    Science.gov (United States)

    Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra

    2017-06-01

    Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

  20. Graph theoretical analysis of functional network for comprehension of sign language.

    Science.gov (United States)

    Liu, Lanfang; Yan, Xin; Liu, Jin; Xia, Mingrui; Lu, Chunming; Emmorey, Karen; Chu, Mingyuan; Ding, Guosheng

    2017-09-15

    Signed languages are natural human languages using the visual-motor modality. Previous neuroimaging studies based on univariate activation analysis show that a widely overlapped cortical network is recruited regardless whether the sign language is comprehended (for signers) or not (for non-signers). Here we move beyond previous studies by examining whether the functional connectivity profiles and the underlying organizational structure of the overlapped neural network may differ between signers and non-signers when watching sign language. Using graph theoretical analysis (GTA) and fMRI, we compared the large-scale functional network organization in hearing signers with non-signers during the observation of sentences in Chinese Sign Language. We found that signed sentences elicited highly similar cortical activations in the two groups of participants, with slightly larger responses within the left frontal and left temporal gyrus in signers than in non-signers. Crucially, further GTA revealed substantial group differences in the topologies of this activation network. Globally, the network engaged by signers showed higher local efficiency (t (24) =2.379, p=0.026), small-worldness (t (24) =2.604, p=0.016) and modularity (t (24) =3.513, p=0.002), and exhibited different modular structures, compared to the network engaged by non-signers. Locally, the left ventral pars opercularis served as a network hub in the signer group but not in the non-signer group. These findings suggest that, despite overlap in cortical activation, the neural substrates underlying sign language comprehension are distinguishable at the network level from those for the processing of gestural action. Copyright © 2017 Elsevier B.V. All rights reserved.

  1. A Distributed Spanning Tree Algorithm

    DEFF Research Database (Denmark)

    Johansen, Karl Erik; Jørgensen, Ulla Lundin; Nielsen, Sven Hauge

    We present a distributed algorithm for constructing a spanning tree for connected undirected graphs. Nodes correspond to processors and edges correspond to two-way channels. Each processor has initially a distinct identity and all processors perform the same algorithm. Computation as well...

  2. Scaling Techniques for Massive Scale-Free Graphs in Distributed (External) Memory

    KAUST Repository

    Pearce, Roger

    2013-05-01

    We present techniques to process large scale-free graphs in distributed memory. Our aim is to scale to trillions of edges, and our research is targeted at leadership class supercomputers and clusters with local non-volatile memory, e.g., NAND Flash. We apply an edge list partitioning technique, designed to accommodate high-degree vertices (hubs) that create scaling challenges when processing scale-free graphs. In addition to partitioning hubs, we use ghost vertices to represent the hubs to reduce communication hotspots. We present a scaling study with three important graph algorithms: Breadth-First Search (BFS), K-Core decomposition, and Triangle Counting. We also demonstrate scalability on BG/P Intrepid by comparing to best known Graph500 results. We show results on two clusters with local NVRAM storage that are capable of traversing trillion-edge scale-free graphs. By leveraging node-local NAND Flash, our approach can process thirty-two times larger datasets with only a 39% performance degradation in Traversed Edges Per Second (TEPS). © 2013 IEEE.

  3. GRAPES: a software for parallel searching on biological graphs targeting multi-core architectures.

    Directory of Open Access Journals (Sweden)

    Rosalba Giugno

    Full Text Available Biological applications, from genomics to ecology, deal with graphs that represents the structure of interactions. Analyzing such data requires searching for subgraphs in collections of graphs. This task is computationally expensive. Even though multicore architectures, from commodity computers to more advanced symmetric multiprocessing (SMP, offer scalable computing power, currently published software implementations for indexing and graph matching are fundamentally sequential. As a consequence, such software implementations (i do not fully exploit available parallel computing power and (ii they do not scale with respect to the size of graphs in the database. We present GRAPES, software for parallel searching on databases of large biological graphs. GRAPES implements a parallel version of well-established graph searching algorithms, and introduces new strategies which naturally lead to a faster parallel searching system especially for large graphs. GRAPES decomposes graphs into subcomponents that can be efficiently searched in parallel. We show the performance of GRAPES on representative biological datasets containing antiviral chemical compounds, DNA, RNA, proteins, protein contact maps and protein interactions networks.

  4. Reconfiguring Independent Sets in Claw-Free Graphs

    NARCIS (Netherlands)

    Bonsma, P.S.; Kamiński, Marcin; Wrochna, Marcin; Ravi, R.; Gørtz, Inge Li

    We present a polynomial-time algorithm that, given two independent sets in a claw-free graph G, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S and to add a new vertex w (not in

  5. VLSI PARTITIONING ALGORITHM WITH ADAPTIVE CONTROL PARAMETER

    Directory of Open Access Journals (Sweden)

    P. N. Filippenko

    2013-03-01

    Full Text Available The article deals with the problem of very large-scale integration circuit partitioning. A graph is selected as a mathematical model describing integrated circuit. Modification of ant colony optimization algorithm is presented, which is used to solve graph partitioning problem. Ant colony optimization algorithm is an optimization method based on the principles of self-organization and other useful features of the ants’ behavior. The proposed search system is based on ant colony optimization algorithm with the improved method of the initial distribution and dynamic adjustment of the control search parameters. The experimental results and performance comparison show that the proposed method of very large-scale integration circuit partitioning provides the better search performance over other well known algorithms.

  6. Algorithm for complete enumeration based on a stroke graph to solve the supply network configuration and operations scheduling problem

    Directory of Open Access Journals (Sweden)

    Julien Maheut

    2013-07-01

    Full Text Available Purpose: The purpose of this paper is to present an algorithm that solves the supply network configuration and operations scheduling problem in a mass customization company that faces alternative operations for one specific tool machine order in a multiplant context. Design/methodology/approach: To achieve this objective, the supply chain network configuration and operations scheduling problem is presented. A model based on stroke graphs allows the design of an algorithm that enumerates all the feasible solutions. The algorithm considers the arrival of a new customized order proposal which has to be inserted into a scheduled program. A selection function is then used to choose the solutions to be simulated in a specific simulation tool implemented in a Decision Support System. Findings and Originality/value: The algorithm itself proves efficient to find all feasible solutions when alternative operations must be considered. The stroke structure is successfully used to schedule operations when considering more than one manufacturing and supply option in each step. Research limitations/implications: This paper includes only the algorithm structure for a one-by-one, sequenced introduction of new products into the list of units to be manufactured. Therefore, the lotsizing process is done on a lot-per-lot basis. Moreover, the validation analysis is done through a case study and no generalization can be done without risk. Practical implications: The result of this research would help stakeholders to determine all the feasible and practical solutions for their problem. It would also allow to assessing the total costs and delivery times of each solution. Moreover, the Decision Support System proves useful to assess alternative solutions. Originality/value: This research offers a simple algorithm that helps solve the supply network configuration problem and, simultaneously, the scheduling problem by considering alternative operations. The proposed system

  7. The parametric modified limited penetrable visibility graph for constructing complex networks from time series

    Science.gov (United States)

    Li, Xiuming; Sun, Mei; Gao, Cuixia; Han, Dun; Wang, Minggang

    2018-02-01

    This paper presents the parametric modified limited penetrable visibility graph (PMLPVG) algorithm for constructing complex networks from time series. We modify the penetrable visibility criterion of limited penetrable visibility graph (LPVG) in order to improve the rationality of the original penetrable visibility and preserve the dynamic characteristics of the time series. The addition of view angle provides a new approach to characterize the dynamic structure of the time series that is invisible in the previous algorithm. The reliability of the PMLPVG algorithm is verified by applying it to three types of artificial data as well as the actual data of natural gas prices in different regions. The empirical results indicate that PMLPVG algorithm can distinguish the different time series from each other. Meanwhile, the analysis results of natural gas prices data using PMLPVG are consistent with the detrended fluctuation analysis (DFA). The results imply that the PMLPVG algorithm may be a reasonable and significant tool for identifying various time series in different fields.

  8. A distributed spanning tree algorithm

    DEFF Research Database (Denmark)

    Johansen, Karl Erik; Jørgensen, Ulla Lundin; Nielsen, Svend Hauge

    1988-01-01

    We present a distributed algorithm for constructing a spanning tree for connected undirected graphs. Nodes correspond to processors and edges correspond to two way channels. Each processor has initially a distinct identity and all processors perform the same algorithm. Computation as well as comm...

  9. Quantifying motor recovery after stroke using independent vector analysis and graph-theoretical analysis

    Directory of Open Access Journals (Sweden)

    Jonathan Laney

    2015-01-01

    Full Text Available The assessment of neuroplasticity after stroke through functional magnetic resonance imaging (fMRI analysis is a developing field where the objective is to better understand the neural process of recovery and to better target rehabilitation interventions. The challenge in this population stems from the large amount of individual spatial variability and the need to summarize entire brain maps by generating simple, yet discriminating features to highlight differences in functional connectivity. Independent vector analysis (IVA has been shown to provide superior performance in preserving subject variability when compared with widely used methods such as group independent component analysis. Hence, in this paper, graph-theoretical (GT analysis is applied to IVA-generated components to effectively exploit the individual subjects' connectivity to produce discriminative features. The analysis is performed on fMRI data collected from individuals with chronic stroke both before and after a 6-week arm and hand rehabilitation intervention. Resulting GT features are shown to capture connectivity changes that are not evident through direct comparison of the group t-maps. The GT features revealed increased small worldness across components and greater centrality in key motor networks as a result of the intervention, suggesting improved efficiency in neural communication. Clinically, these results bring forth new possibilities as a means to observe the neural processes underlying improvements in motor function.

  10. Optimizing spread dynamics on graphs by message passing

    International Nuclear Information System (INIS)

    Altarelli, F; Braunstein, A; Dall’Asta, L; Zecchina, R

    2013-01-01

    Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network). (paper)

  11. Optimizing spread dynamics on graphs by message passing

    Science.gov (United States)

    Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.

    2013-09-01

    Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

  12. Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions

    Science.gov (United States)

    Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

    2018-04-01

    In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute

  13. Graph Theory and Ion and Molecular Aggregation in Aqueous Solutions.

    Science.gov (United States)

    Choi, Jun-Ho; Lee, Hochan; Choi, Hyung Ran; Cho, Minhaeng

    2018-04-20

    In molecular and cellular biology, dissolved ions and molecules have decisive effects on chemical and biological reactions, conformational stabilities, and functions of small to large biomolecules. Despite major efforts, the current state of understanding of the effects of specific ions, osmolytes, and bioprotecting sugars on the structure and dynamics of water H-bonding networks and proteins is not yet satisfactory. Recently, to gain deeper insight into this subject, we studied various aggregation processes of ions and molecules in high-concentration salt, osmolyte, and sugar solutions with time-resolved vibrational spectroscopy and molecular dynamics simulation methods. It turns out that ions (or solute molecules) have a strong propensity to self-assemble into large and polydisperse aggregates that affect both local and long-range water H-bonding structures. In particular, we have shown that graph-theoretical approaches can be used to elucidate morphological characteristics of large aggregates in various aqueous salt, osmolyte, and sugar solutions. When ion and molecular aggregates in such aqueous solutions are treated as graphs, a variety of graph-theoretical properties, such as graph spectrum, degree distribution, clustering coefficient, minimum path length, and graph entropy, can be directly calculated by considering an ensemble of configurations taken from molecular dynamics trajectories. Here we show percolating behavior exhibited by ion and molecular aggregates upon increase in solute concentration in high solute concentrations and discuss compelling evidence of the isomorphic relation between percolation transitions of ion and molecular aggregates and water H-bonding networks. We anticipate that the combination of graph theory and molecular dynamics simulation methods will be of exceptional use in achieving a deeper understanding of the fundamental physical chemistry of dissolution and in describing the interplay between the self-aggregation of solute

  14. Random broadcast on random geometric graphs

    Energy Technology Data Exchange (ETDEWEB)

    Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY

    2009-01-01

    In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.

  15. Chromatic graph theory

    CERN Document Server

    Chartrand, Gary; Rosen, Kenneth H

    2008-01-01

    Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...

  16. Spectral Methods for Immunization of Large Networks

    Directory of Open Access Journals (Sweden)

    Muhammad Ahmad

    2017-11-01

    Full Text Available Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbour nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constraint that are immunized (vaccinated, screened, filtered so as the remaining graph is less prone to the epidemic. It is known that the problem is, in all practical models, computationally intractable even for moderate sized graphs. In this paper we employ ideas from spectral graph theory to define relevance and importance of nodes. Using novel graph theoretic techniques, we then design an efficient approximation algorithm to immunize the graph. Theoretical guarantees on the running time of our algorithm show that it is more efficient than any other known solution in the literature. We test the performance of our algorithm on several real world graphs. Experiments show that our algorithm scales well for large graphs and outperforms state of the art algorithms both in quality (containment of epidemic and efficiency (runtime and space complexity.

  17. A theoretically exact reconstruction algorithm for helical cone-beam differential phase-contrast computed tomography

    International Nuclear Information System (INIS)

    Li Jing; Sun Yi; Zhu Peiping

    2013-01-01

    Differential phase-contrast computed tomography (DPC-CT) reconstruction problems are usually solved by using parallel-, fan- or cone-beam algorithms. For rod-shaped objects, the x-ray beams cannot recover all the slices of the sample at the same time. Thus, if a rod-shaped sample is required to be reconstructed by the above algorithms, one should alternately perform translation and rotation on this sample, which leads to lower efficiency. The helical cone-beam CT may significantly improve scanning efficiency for rod-shaped objects over other algorithms. In this paper, we propose a theoretically exact filter-backprojection algorithm for helical cone-beam DPC-CT, which can be applied to reconstruct the refractive index decrement distribution of the samples directly from two-dimensional differential phase-contrast images. Numerical simulations are conducted to verify the proposed algorithm. Our work provides a potential solution for inspecting the rod-shaped samples using DPC-CT, which may be applicable with the evolution of DPC-CT equipments. (paper)

  18. A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

    Science.gov (United States)

    He, Chenlong; Feng, Zuren; Ren, Zhigang

    2018-01-01

    In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

  19. A flocking algorithm for multi-agent systems with connectivity preservation under hybrid metric-topological interactions.

    Directory of Open Access Journals (Sweden)

    Chenlong He

    Full Text Available In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.

  20. Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time

    DEFF Research Database (Denmark)

    Wulff-Nilsen, Christian

    2008-01-01

    We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log...

  1. A hierarchical graph neuron scheme for real-time pattern recognition.

    Science.gov (United States)

    Nasution, B B; Khan, A I

    2008-02-01

    The hierarchical graph neuron (HGN) implements a single cycle memorization and recall operation through a novel algorithmic design. The HGN is an improvement on the already published original graph neuron (GN) algorithm. In this improved approach, it recognizes incomplete/noisy patterns. It also resolves the crosstalk problem, which is identified in the previous publications, within closely matched patterns. To accomplish this, the HGN links multiple GN networks for filtering noise and crosstalk out of pattern data inputs. Intrinsically, the HGN is a lightweight in-network processing algorithm which does not require expensive floating point computations; hence, it is very suitable for real-time applications and tiny devices such as the wireless sensor networks. This paper describes that the HGN's pattern matching capability and the small response time remain insensitive to the increases in the number of stored patterns. Moreover, the HGN does not require definition of rules or setting of thresholds by the operator to achieve the desired results nor does it require heuristics entailing iterative operations for memorization and recall of patterns.

  2. Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus

    Science.gov (United States)

    Buring, Ricardo; Kiselev, Arthemy V.; Rutten, Nina

    2018-02-01

    Let \\mathscr{P} be a Poisson structure on a finite-dimensional affine real manifold. Can \\mathscr{P} be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach - with respect to all affine Poisson manifolds - to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.

  3. Building Scalable Knowledge Graphs for Earth Science

    Science.gov (United States)

    Ramachandran, R.; Maskey, M.; Gatlin, P. N.; Zhang, J.; Duan, X.; Bugbee, K.; Christopher, S. A.; Miller, J. J.

    2017-12-01

    Estimates indicate that the world's information will grow by 800% in the next five years. In any given field, a single researcher or a team of researchers cannot keep up with this rate of knowledge expansion without the help of cognitive systems. Cognitive computing, defined as the use of information technology to augment human cognition, can help tackle large systemic problems. Knowledge graphs, one of the foundational components of cognitive systems, link key entities in a specific domain with other entities via relationships. Researchers could mine these graphs to make probabilistic recommendations and to infer new knowledge. At this point, however, there is a dearth of tools to generate scalable Knowledge graphs using existing corpus of scientific literature for Earth science research. Our project is currently developing an end-to-end automated methodology for incrementally constructing Knowledge graphs for Earth Science. Semantic Entity Recognition (SER) is one of the key steps in this methodology. SER for Earth Science uses external resources (including metadata catalogs and controlled vocabulary) as references to guide entity extraction and recognition (i.e., labeling) from unstructured text, in order to build a large training set to seed the subsequent auto-learning component in our algorithm. Results from several SER experiments will be presented as well as lessons learned.

  4. Sampling Large Graphs for Anticipatory Analytics

    Science.gov (United States)

    2015-05-15

    low. C. Random Area Sampling Random area sampling [8] is a “ snowball ” sampling method in which a set of random seed vertices are selected and areas... Sampling Large Graphs for Anticipatory Analytics Lauren Edwards, Luke Johnson, Maja Milosavljevic, Vijay Gadepally, Benjamin A. Miller Lincoln...systems, greater human-in-the-loop involvement, or through complex algorithms. We are investigating the use of sampling to mitigate these challenges

  5. Poor textural image tie point matching via graph theory

    Science.gov (United States)

    Yuan, Xiuxiao; Chen, Shiyu; Yuan, Wei; Cai, Yang

    2017-07-01

    Feature matching aims to find corresponding points to serve as tie points between images. Robust matching is still a challenging task when input images are characterized by low contrast or contain repetitive patterns, occlusions, or homogeneous textures. In this paper, a novel feature matching algorithm based on graph theory is proposed. This algorithm integrates both geometric and radiometric constraints into an edge-weighted (EW) affinity tensor. Tie points are then obtained by high-order graph matching. Four pairs of poor textural images covering forests, deserts, bare lands, and urban areas are tested. For comparison, three state-of-the-art matching techniques, namely, scale-invariant feature transform (SIFT), speeded up robust features (SURF), and features from accelerated segment test (FAST), are also used. The experimental results show that the matching recall obtained by SIFT, SURF, and FAST varies from 0 to 35% in different types of poor textures. However, through the integration of both geometry and radiometry and the EW strategy, the recall obtained by the proposed algorithm is better than 50% in all four image pairs. The better matching recall improves the number of correct matches, dispersion, and positional accuracy.

  6. INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

    Energy Technology Data Exchange (ETDEWEB)

    Groer, Christopher S [ORNL; Sullivan, Blair D [ORNL; Weerapurage, Dinesh P [ORNL

    2012-10-01

    It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some \\emph{NP}-hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.

  7. Computation of watersheds based on parallel graph algorithms

    NARCIS (Netherlands)

    Meijster, A.; Roerdink, J.B.T.M.; Maragos, P; Schafer, RW; Butt, MA

    1996-01-01

    In this paper the implementation of a parallel watershed algorithm is described. The algorithm has been implemented on a Cray J932, which is a shared memory architecture with 32 processors. The watershed transform has generally been considered to be inherently sequential, but recently a few research

  8. Co-clustering directed graphs to discover asymmetries and directional communities.

    Science.gov (United States)

    Rohe, Karl; Qin, Tai; Yu, Bin

    2016-10-21

    In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.

  9. A characterization of horizontal visibility graphs and combinatorics on words

    Science.gov (United States)

    Gutin, Gregory; Mansour, Toufik; Severini, Simone

    2011-06-01

    A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.

  10. Graph-Based Semantic Web Service Composition for Healthcare Data Integration.

    Science.gov (United States)

    Arch-Int, Ngamnij; Arch-Int, Somjit; Sonsilphong, Suphachoke; Wanchai, Paweena

    2017-01-01

    Within the numerous and heterogeneous web services offered through different sources, automatic web services composition is the most convenient method for building complex business processes that permit invocation of multiple existing atomic services. The current solutions in functional web services composition lack autonomous queries of semantic matches within the parameters of web services, which are necessary in the composition of large-scale related services. In this paper, we propose a graph-based Semantic Web Services composition system consisting of two subsystems: management time and run time. The management-time subsystem is responsible for dependency graph preparation in which a dependency graph of related services is generated automatically according to the proposed semantic matchmaking rules. The run-time subsystem is responsible for discovering the potential web services and nonredundant web services composition of a user's query using a graph-based searching algorithm. The proposed approach was applied to healthcare data integration in different health organizations and was evaluated according to two aspects: execution time measurement and correctness measurement.

  11. Belief propagation and loop series on planar graphs

    International Nuclear Information System (INIS)

    Chertkov, Michael; Teodorescu, Razvan; Chernyak, Vladimir Y

    2008-01-01

    We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of Chertkov and Chernyak (2006 Phys. Rev. E 73 065102(R) [cond-mat/0601487]; 2006 J. Stat. Mech. P06009 [cond-mat/0603189]) is used to evaluate the resulting series expansion for the partition function. We show that, for planar graphs, truncating the series at single-connected loops reduces, via a map reminiscent of the Fisher transformation (Fisher 1961 Phys. Rev. 124 1664), to evaluating the partition function of the dimer-matching model on an auxiliary planar graph. Thus, the truncated series can be easily re-summed, using the Pfaffian formula of Kasteleyn (1961 Physics 27 1209). This allows us to identify a big class of computationally tractable planar models reducible to a dimer model via the Belief Propagation (gauge) transformation. The Pfaffian representation can also be extended to the full Loop Series, in which case the expansion becomes a sum of Pfaffian contributions, each associated with dimer matchings on an extension to a subgraph of the original graph. Algorithmic consequences of the Pfaffian representation, as well as relations to quantum and non-planar models, are discussed

  12. EIT Imaging Regularization Based on Spectral Graph Wavelets.

    Science.gov (United States)

    Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

    2017-09-01

    The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

  13. Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

    Directory of Open Access Journals (Sweden)

    Thomas J. Marlowe

    1998-01-01

    Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants.

  14. A simple method for finding the scattering coefficients of quantum graphs

    International Nuclear Information System (INIS)

    Cottrell, Seth S.

    2015-01-01

    Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial of the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected

  15. Indexing molecules with chemical graph identifiers.

    Science.gov (United States)

    Gregori-Puigjané, Elisabet; Garriga-Sust, Rut; Mestres, Jordi

    2011-09-01

    Fast and robust algorithms for indexing molecules have been historically considered strategic tools for the management and storage of large chemical libraries. This work introduces a modified and further extended version of the molecular equivalence number naming adaptation of the Morgan algorithm (J Chem Inf Comput Sci 2001, 41, 181-185) for the generation of a chemical graph identifier (CGI). This new version corrects for the collisions recognized in the original adaptation and includes the ability to deal with graph canonicalization, ensembles (salts), and isomerism (tautomerism, regioisomerism, optical isomerism, and geometrical isomerism) in a flexible manner. Validation of the current CGI implementation was performed on the open NCI database and the drug-like subset of the ZINC database containing 260,071 and 5,348,089 structures, respectively. The results were compared with those obtained with some of the most widely used indexing codes, such as the CACTVS hash code and the new InChIKey. The analyses emphasize the fact that compound management activities, like duplicate analysis of chemical libraries, are sensitive to the exact definition of compound uniqueness and thus still depend, to a minor extent, on the type and flexibility of the molecular index being used. Copyright © 2011 Wiley Periodicals, Inc.

  16. Graph sampling

    OpenAIRE

    Zhang, L.-C.; Patone, M.

    2017-01-01

    We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.

  17. Minimum Covers of Fixed Cardinality in Weighted Graphs.

    Science.gov (United States)

    White, Lee J.

    Reported is the result of research on combinatorial and algorithmic techniques for information processing. A method is discussed for obtaining minimum covers of specified cardinality from a given weighted graph. By the indicated method, it is shown that the family of minimum covers of varying cardinality is related to the minimum spanning tree of…

  18. Groups, graphs and random walks

    CERN Document Server

    Salvatori, Maura; Sava-Huss, Ecaterina

    2017-01-01

    An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...

  19. Image segmentation algorithm based on T-junctions cues

    Science.gov (United States)

    Qian, Yanyu; Cao, Fengyun; Wang, Lu; Yang, Xuejie

    2016-03-01

    To improve the over-segmentation and over-merge phenomenon of single image segmentation algorithm,a novel approach of combing Graph-Based algorithm and T-junctions cues is proposed in this paper. First, a method by L0 gradient minimization is applied to the smoothing of the target image eliminate artifacts caused by noise and texture detail; Then, the initial over-segmentation result of the smoothing image using the graph-based algorithm; Finally, the final results via a region fusion strategy by t-junction cues. Experimental results on a variety of images verify the new approach's efficiency in eliminating artifacts caused by noise,segmentation accuracy and time complexity has been significantly improved.

  20. Labeling RDF Graphs for Linear Time and Space Querying

    Science.gov (United States)

    Furche, Tim; Weinzierl, Antonius; Bry, François

    Indices and data structures for web querying have mostly considered tree shaped data, reflecting the view of XML documents as tree-shaped. However, for RDF (and when querying ID/IDREF constraints in XML) data is indisputably graph-shaped. In this chapter, we first study existing indexing and labeling schemes for RDF and other graph datawith focus on support for efficient adjacency and reachability queries. For XML, labeling schemes are an important part of the widespread adoption of XML, in particular for mapping XML to existing (relational) database technology. However, the existing indexing and labeling schemes for RDF (and graph data in general) sacrifice one of the most attractive properties of XML labeling schemes, the constant time (and per-node space) test for adjacency (child) and reachability (descendant). In the second part, we introduce the first labeling scheme for RDF data that retains this property and thus achieves linear time and space processing of acyclic RDF queries on a significantly larger class of graphs than previous approaches (which are mostly limited to tree-shaped data). Finally, we show how this labeling scheme can be applied to (acyclic) SPARQL queries to obtain an evaluation algorithm with time and space complexity linear in the number of resources in the queried RDF graph.