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.
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.
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.
Planar graphs theory and algorithms
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.
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...
A cluster algorithm for graphs
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)
Graph Algorithm Animation with Grrr
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...
Gems of combinatorial optimization and graph algorithms
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 ...
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 ...
A new cluster algorithm for graphs
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
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...
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 Â¿(P) in parallel I/O complexity and parallel computation time, compared to the single-processor external memory counterparts....
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.
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.
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.
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.
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.
Discrete geometric analysis of message passing algorithm on graphs
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.
Executable Pseudocode for Graph Algorithms
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
Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs
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.
Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs
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.
Algorithms and Models for the Web Graph
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
Graph-theoretic techniques for web content mining
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.
Optimizing graph algorithms on pregel-like systems
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
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
Analysis and enumeration algorithms for biological graphs
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...
A general algorithm for distributing information in a graph
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.
Neural complexity: A graph theoretic interpretation
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.
A Faster Algorithm for Computing Motorcycle Graphs
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.
A Faster Algorithm for Computing Motorcycle Graphs
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.
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
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
Unsupervised active learning based on hierarchical graph-theoretic clustering.
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.
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.
Optimizing graph algorithms on pregel-like systems
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.
Scalable force directed graph layout algorithms using fast multipole methods
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
Graph-theoretic approach to quantum correlations.
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.
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...
Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs
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.
Efficient Algorithmic Frameworks via Structural Graph Theory
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
Graph theoretical model of a sensorimotor connectome in zebrafish.
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.
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.
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...
A hierarchical approach to reducing communication in parallel graph algorithms
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
Evaluation of Static JavaScript Call Graph Algorithms
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
Exact parallel maximum clique algorithm for general and protein graphs.
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.
Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs
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
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.
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
Scalable force directed graph layout algorithms using fast multipole methods
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.
Connectivity algorithm with depth first search (DFS) on simple graphs
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).
A novel line segment detection algorithm based on graph search
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).
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.
BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.
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
Fitchi: haplotype genealogy graphs based on the Fitch algorithm.
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.
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.
A hierarchical approach to reducing communication in parallel graph algorithms
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.
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.
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....
Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data
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 ...
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....
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)
Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination
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
Parallel Algorithms for Switching Edges in Heterogeneous Graphs.
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.
Low-algorithmic-complexity entropy-deceiving graphs
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.
Low-algorithmic-complexity entropy-deceiving graphs
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.
Modification of MSDR algorithm and ITS implementation on graph clustering
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.
Graph-drawing algorithms geometries versus molecular mechanics in fullereness
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.
Development of antibiotic regimens using graph based evolutionary algorithms.
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.
Graph theoretical analysis of EEG functional connectivity during music perception.
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.
A Faster Algorithm to Recognize Even-Hole-Free Graphs
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...
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.
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
On the design of a hierarchical SS7 network: A graph theoretical approach
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.
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
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.
Dynamic Programming and Graph Algorithms in Computer Vision*
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
Tractable Algorithms for Proximity Search on Large Graphs
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
Unwinding the hairball graph: Pruning algorithms for weighted complex networks
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.
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.
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)
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.
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
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.
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.
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...
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
Time- and Cost-Optimal Parallel Algorithms for the Dominance and Visibility Graphs
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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.
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
Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs
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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
Efficient parallel and out of core algorithms for constructing large bi-directed de Bruijn graphs.
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
Graph-based clustering and data visualization algorithms
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
A Graph Summarization Algorithm Based on RFID Logistics
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.
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.'
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
Algorithm for shortest path search in Geographic Information Systems by using reduced graphs.
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.
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
Directory of Open Access Journals (Sweden)
S. Venkatesh
2012-01-01
Full Text Available Partial discharge (PD is a major cause of failure of power apparatus and hence its measurement and analysis have emerged as a vital field in assessing the condition of the insulation system. Several efforts have been undertaken by researchers to classify PD pulses utilizing artificial intelligence techniques. Recently, the focus has shifted to the identification of multiple sources of PD since it is often encountered in real-time measurements. Studies have indicated that classification of multi-source PD becomes difficult with the degree of overlap and that several techniques such as mixed Weibull functions, neural networks, and wavelet transformation have been attempted with limited success. Since digital PD acquisition systems record data for a substantial period, the database becomes large, posing considerable difficulties during classification. This research work aims firstly at analyzing aspects concerning classification capability during the discrimination of multisource PD patterns. Secondly, it attempts at extending the previous work of the authors in utilizing the novel approach of probabilistic neural network versions for classifying moderate sets of PD sources to that of large sets. The third focus is on comparing the ability of partition-based algorithms, namely, the labelled (learning vector quantization and unlabelled (K-means versions, with that of a novel hypergraph-based clustering method in providing parsimonious sets of centers during classification.
Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data.
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.
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...
A Graph-Algorithmic Approach for the Study of Metastability in Markov Chains
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.
A graph theoretical perspective of a drug abuse epidemic model
Nyabadza, F.; Mukwembi, S.; Rodrigues, B. G.
2011-05-01
A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, i.e., the proportion of the individual’s drug user contacts who are not in treatment amongst all of his or her contacts. We introduce parameters α∗, β∗ and γ∗, depending on the neighbourhood prevalence, which govern the spread of drug use. We examine how changes in α∗, β∗ and γ∗ affect the system dynamics. Simulations presented support the theoretical results.
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
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)
Theoretical Bound of CRLB for Energy Efficient Technique of RSS-Based Factor Graph Geolocation
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.
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)
Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
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.
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.)
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.
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
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.
GraDit: graph-based data repair algorithm for multiple data edits rule violations
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.
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.
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.
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.
Computation of watersheds based on parallel graph algorithms
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
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...
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....
External Memory Graph Algorithms and Range Searching Data Structures
DEFF Research Database (Denmark)
Walderveen, Freek van
). In order to present (for example geographic) data to a user, it is often necessary to select only a relatively small part of a dataset|such as all post oces in the region visible on the user's screen|and return some statictic about this part|such as the distance between the two furthest post oces...... in the region, which may help a postal company in determining what delivery time they can guarantee for their customers. Even in non-geometric settings, the part of the data that needs to be selected is often easily described geometrically, for example in database queries asking for records matching multiple......Every day larger amounts of data are generated that describe our world in terms of networks or graphs. Think for example about maps of roads or rivers, social networks, or the internet (either as a network of computers or as a network of hyperlinks). Besides this, also surface models...
Personalized PageRank Clustering: A graph clustering algorithm based on random walks
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.
Multi-scale graph-cut algorithm for efficient water-fat separation.
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.
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.
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.
Graph theoretical stable allocation as a tool for reproduction of control by human operators
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.
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.
An effective trust-based recommendation method using a novel graph clustering algorithm
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.
A graph-Laplacian-based feature extraction algorithm for neural spike sorting.
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.
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.
Design of application for graph's handling with heuristic algorithms of analysis
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.
Generalized connectivity of graphs
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.
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 ...
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.
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.
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.
Guidelines for a graph-theoretic implementation of structural equation modeling
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
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.
Bladder segmentation in MR images with watershed segmentation and graph cut algorithm
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.
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.
PAGANI Toolkit: Parallel graph-theoretical analysis package for brain network big data.
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.
Abnormalities of functional brain networks in pathological gambling: a graph-theoretical approach
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
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.
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.
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.
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
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.
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.
Directory of Open Access Journals (Sweden)
Guimarães Katia S
2006-04-01
Full Text Available Abstract Background Most cellular processes are carried out by multi-protein complexes, groups of proteins that bind together to perform a specific task. Some proteins form stable complexes, while other proteins form transient associations and are part of several complexes at different stages of a cellular process. A better understanding of this higher-order organization of proteins into overlapping complexes is an important step towards unveiling functional and evolutionary mechanisms behind biological networks. Results We propose a new method for identifying and representing overlapping protein complexes (or larger units called functional groups within a protein interaction network. We develop a graph-theoretical framework that enables automatic construction of such representation. We illustrate the effectiveness of our method by applying it to TNFα/NF-κB and pheromone signaling pathways. Conclusion The proposed representation helps in understanding the transitions between functional groups and allows for tracking a protein's path through a cascade of functional groups. Therefore, depending on the nature of the network, our representation is capable of elucidating temporal relations between functional groups. Our results show that the proposed method opens a new avenue for the analysis of protein interaction networks.
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.
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.
Hindumathi, V; Kranthi, T; Rao, S B; Manimaran, P
2014-06-01
With rapidly changing technology, prediction of candidate genes has become an indispensable task in recent years mainly in the field of biological research. The empirical methods for candidate gene prioritization that succors to explore the potential pathway between genetic determinants and complex diseases are highly cumbersome and labor intensive. In such a scenario predicting potential targets for a disease state through in silico approaches are of researcher's interest. The prodigious availability of protein interaction data coupled with gene annotation renders an ease in the accurate determination of disease specific candidate genes. In our work we have prioritized the cervix related cancer candidate genes by employing Csaba Ortutay and his co-workers approach of identifying the candidate genes through graph theoretical centrality measures and gene ontology. With the advantage of the human protein interaction data, cervical cancer gene sets and the ontological terms, we were able to predict 15 novel candidates for cervical carcinogenesis. The disease relevance of the anticipated candidate genes was corroborated through a literature survey. Also the presence of the drugs for these candidates was detected through Therapeutic Target Database (TTD) and DrugMap Central (DMC) which affirms that they may be endowed as potential drug targets for cervical cancer.
Topological properties of the limited penetrable horizontal visibility graph family
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.
Digital Geometry Algorithms Theoretical Foundations and Applications to Computational Imaging
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.
Graph theoretical analysis of functional network for comprehension of sign language.
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.
Wang, Chao; Xu, Jin; Zhao, Songzhen; Lou, Wutao
2016-01-01
The study was dedicated to investigating the change in information processing in brain networks of vascular dementia (VaD) patients during the process of decision making. EEG was recorded from 18 VaD patients and 19 healthy controls when subjects were performing a visual oddball task. The whole task was divided into several stages by using global field power analysis. In the stage related to the decision-making process, graph theoretical analysis was applied to the binary directed network derived from EEG signals at nine electrodes in the frontal, central, and parietal regions in δ (0.5-3.5Hz), θ (4-7Hz), α1 (8-10Hz), α2 (11-13Hz), and β (14-30Hz) frequency bands based on directed transfer function. A weakened outgoing information flow, a decrease in out-degree, and an increase in in-degree were found in the parietal region in VaD patients, compared to healthy controls. In VaD patients, the parietal region may also lose its hub status in brain networks. In addition, the clustering coefficient was significantly lower in VaD patients. Impairment might be present in the parietal region or its connections with other regions, and it may serve as one of the causes for cognitive decline in VaD patients. The brain networks of VaD patients were significantly altered toward random networks. The present study extended our understanding of VaD from the perspective of brain functional networks, and it provided possible interpretations for cognitive deficits in VaD patients. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Jun Lv
Full Text Available Functional brain networks of human have been revealed to have small-world properties by both analyzing electroencephalogram (EEG and functional magnetic resonance imaging (fMRI time series.In our study, by using graph theoretical analysis, we attempted to investigate the changes of paralimbic-limbic cortex between wake and sleep states. Ten healthy young people were recruited to our experiment. Data from 2 subjects were excluded for the reason that they had not fallen asleep during the experiment. For each subject, blood oxygen level dependency (BOLD images were acquired to analyze brain network, and peripheral pulse signals were obtained continuously to identify if the subject was in sleep periods. Results of fMRI showed that brain networks exhibited stronger small-world characteristics during sleep state as compared to wake state, which was in consistent with previous studies using EEG synchronization. Moreover, we observed that compared with wake state, paralimbic-limbic cortex had less connectivity with neocortical system and centrencephalic structure in sleep.In conclusion, this is the first study, to our knowledge, has observed that small-world properties of brain functional networks altered when human sleeps without EEG synchronization. Moreover, we speculate that paralimbic-limbic cortex organization owns an efficient defense mechanism responsible for suppressing the external environment interference when humans sleep, which is consistent with the hypothesis that the paralimbic-limbic cortex may be functionally disconnected from brain regions which directly mediate their interactions with the external environment. Our findings also provide a reasonable explanation why stable sleep exhibits homeostasis which is far less susceptible to outside world.
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
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
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.
A scalable community detection algorithm for large graphs using stochastic block models
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
A scalable community detection algorithm for large graphs using stochastic block models
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
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.
The Mathematics of Networks Science: Scale-Free, Power-Law Graphs and Continuum Theoretical Analysis
Padula, Janice
2012-01-01
When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date,…
Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms
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...
International Nuclear Information System (INIS)
Randic, M.; Wilkins, C.L.
1979-01-01
Selected molecular data on alkanes have been reexamined in a search for general regularities in isomeric variations. In contrast to the prevailing approaches concerned with fitting data by searching for optimal parameterization, the present work is primarily aimed at established trends, i.e., searching for relative magnitudes and their regularities among the isomers. Such an approach is complementary to curve fitting or correlation seeking procedures. It is particularly useful when there are incomplete data which allow trends to be recognized but no quantitative correlation to be established. One proceeds by first ordering structures. One way is to consider molecular graphs and enumerate paths of different length as the basic graph invariant. It can be shown that, for several thermodynamic molecular properties, the number of paths of length two (p 2 ) and length three (p 3 ) are critical. Hence, an ordering based on p 2 and p 3 indicates possible trends and behavior for many molecular properties, some of which relate to others, some which do not. By considering a grid graph derived by attributing to each isomer coordinates (p 2 ,p 3 ) and connecting points along the coordinate axis, one obtains a simple presentation useful for isomer structural interrelations. This skeletal frame is one upon which possible trends for different molecular properties may be conveniently represented. The significance of the results and their conceptual value is discussed. 16 figures, 3 tables
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.
A linear time algorithm for minimum fill-in and treewidth for distance heredity graphs
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
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.
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...
OpenMP Parallelization and Optimization of Graph-based Machine Learning Algorithms
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
The Algorithm Theoretical Basis Document for Tidal Corrections
Fricker, Helen A.; Ridgway, Jeff R.; Minster, Jean-Bernard; Yi, Donghui; Bentley, Charles R.`
2012-01-01
This Algorithm Theoretical Basis Document deals with the tidal corrections that need to be applied to range measurements made by the Geoscience Laser Altimeter System (GLAS). These corrections result from the action of ocean tides and Earth tides which lead to deviations from an equilibrium surface. Since the effect of tides is dependent of the time of measurement, it is necessary to remove the instantaneous tide components when processing altimeter data, so that all measurements are made to the equilibrium surface. The three main tide components to consider are the ocean tide, the solid-earth tide and the ocean loading tide. There are also long period ocean tides and the pole tide. The approximate magnitudes of these components are illustrated in Table 1, together with estimates of their uncertainties (i.e. the residual error after correction). All of these components are important for GLAS measurements over the ice sheets since centimeter-level accuracy for surface elevation change detection is required. The effect of each tidal component is to be removed by approximating their magnitude using tidal prediction models. Conversely, assimilation of GLAS measurements into tidal models will help to improve them, especially at high latitudes.
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.
Predicting conversion from MCI to AD using resting-state fMRI, graph theoretical approach and SVM.
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.
Vecchio, Fabrizio; Miraglia, Francesca; Bramanti, Placido; Rossini, Paolo Maria
2014-01-01
Modern analysis of electroencephalographic (EEG) rhythms provides information on dynamic brain connectivity. To test the hypothesis that aging processes modulate the brain connectivity network, EEG recording was conducted on 113 healthy volunteers. They were divided into three groups in accordance with their ages: 36 Young (15-45 years), 46 Adult (50-70 years), and 31 Elderly (>70 years). To evaluate the stability of the investigated parameters, a subgroup of 10 subjects underwent a second EEG recording two weeks later. Graph theory functions were applied to the undirected and weighted networks obtained by the lagged linear coherence evaluated by eLORETA on cortical sources. EEG frequency bands of interest were: delta (2-4 Hz), theta (4-8 Hz), alpha1 (8-10.5 Hz), alpha2 (10.5-13 Hz), beta1 (13-20 Hz), beta2 (20-30 Hz), and gamma (30-40 Hz). The spectral connectivity analysis of cortical sources showed that the normalized Characteristic Path Length (λ) presented the pattern Young > Adult>Elderly in the higher alpha band. Elderly also showed a greater increase in delta and theta bands than Young. The correlation between age and λ showed that higher ages corresponded to higher λ in delta and theta and lower in the alpha2 band; this pattern reflects the age-related modulation of higher (alpha) and decreased (delta) connectivity. The Normalized Clustering coefficient (γ) and small-world network modeling (σ) showed non-significant age-modulation. Evidence from the present study suggests that graph theory can aid in the analysis of connectivity patterns estimated from EEG and can facilitate the study of the physiological and pathological brain aging features of functional connectivity networks.
Fast algorithm for computing complex number-theoretic transforms
Reed, I. S.; Liu, K. Y.; Truong, T. K.
1977-01-01
A high-radix FFT algorithm for computing transforms over FFT, where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
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.
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.
Directory of Open Access Journals (Sweden)
Mario Miler
2014-02-01
Full Text Available In the field of geoinformation and transportation science, the shortest path is calculated on graph data mostly found in road and transportation networks. This data is often stored in various database systems. Many applications dealing with transportation network require calculation of the shortest path. The objective of this research is to compare the performance of Dijkstra shortest path calculation in PostgreSQL (with pgRouting and Neo4j graph database for the purpose of determining if there is any difference regarding the speed of the calculation. Benchmarking was done on commodity hardware using OpenStreetMap road network. The first assumption is that Neo4j graph database would be well suited for the shortest path calculation on transportation networks but this does not come without some cost. Memory proved to be an issue in Neo4j setup when dealing with larger transportation networks.
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.
Analysis of protein-protein interaction networks by means of annotated graph mining algorithms
Rahmani, Hossein
2012-01-01
This thesis discusses solutions to several open problems in Protein-Protein Interaction (PPI) networks with the aid of Knowledge Discovery. PPI networks are usually represented as undirected graphs, with nodes corresponding to proteins and edges representing interactions among protein pairs. A large
A graph rewriting programming language for graph drawing
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...
Generating random networks and graphs
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...
Graph Theoretical Analysis of Developmental Patterns of the White Matter Network
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Zhang eChen
2013-11-01
Full Text Available Understanding the development of human brain organization is critical for gaining insight into how the enhancement of cognitive processes is related to the fine-tuning of the brain network. However, the developmental trajectory of the large-scale white matter (WM network is not fully understood. Here, using graph theory, we examine developmental changes in the organization of WM networks in 180 typically-developing participants. WM networks were constructed using whole brain tractography and 78 cortical regions of interest were extracted from each participant. The subjects were first divided into 5 equal sample size (n=36 groups (early childhood: 6.0-9.7 years; late childhood: 9.8-12.7 years; adolescence: 12.9-17.5 years; young adult: 17.6-21.8 years; adult: 21.9-29.6 years. Most prominent changes in the topological properties of developing brain networks occur at late childhood and adolescence. During late childhood period, the structural brain network showed significant increase in the global efficiency but decrease in modularity, suggesting a shift of topological organization toward a more randomized configuration. However, while preserving most topological features, there was a significant increase in the local efficiency at adolescence, suggesting the dynamic process of rewiring and rebalancing brain connections at different growth stages. In addition, several pivotal hubs were identified that are vital for the global coordination of information flow over the whole brain network across all age groups. Significant increases of nodal efficiency were present in several regions such as precuneus at late childhood. Finally, a stable and functionally/anatomically related modular organization was identified throughout the development of the WM network. This study used network analysis to elucidate the topological changes in brain maturation, paving the way for developing novel methods for analyzing disrupted brain connectivity in
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.
A theoretical analysis of the median LMF adaptive algorithm
DEFF Research Database (Denmark)
Bysted, Tommy Kristensen; Rusu, C.
1999-01-01
Higher order adaptive algorithms are sensitive to impulse interference. In the case of the LMF (Least Mean Fourth), an easy and effective way to reduce this is to median filter the instantaneous gradient of the LMF algorithm. Although previous published simulations have indicated that this reduces...... the speed of convergence, no analytical studies have yet been made to prove this. In order to enhance the usability, this paper presents a convergence and steady-state analysis of the median LMF adaptive algorithm. As expected this proves that the median LMF has a slower convergence and a lower steady...
Use of graph algorithms in the processing and analysis of images with focus on the biomedical data.
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).
Theoretical and numerical study of an optimum design algorithm
International Nuclear Information System (INIS)
Destuynder, Philippe.
1976-08-01
This work can be separated into two main parts. First, the behavior of the solution of an elliptic variational equation is analyzed when the domain is submitted to a small perturbation. The case of inequations is also considered. Secondly the previous results are used for deriving an optimum design algorithm. This algorithm was suggested by the center-method proposed by Huard. Numerical results show the superiority of the method on other different optimization techniques [fr
On characterizing terrain visibility graphs
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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.
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.)
A theoretical derivation of the condensed history algorithm
International Nuclear Information System (INIS)
Larsen, E.W.
1992-01-01
Although the Condensed History Algorithm is a successful and widely-used Monte Carlo method for solving electron transport problems, it has been derived only by an ad-hoc process based on physical reasoning. In this paper we show that the Condensed History Algorithm can be justified as a Monte Carlo simulation of an operator-split procedure in which the streaming, angular scattering, and slowing-down operators are separated within each time step. Different versions of the operator-split procedure lead to Ο(Δs) and Ο(Δs 2 ) versions of the method, where Δs is the path-length step. Our derivation also indicates that higher-order versions of the Condensed History Algorithm may be developed. (Author)
A Comparison of SLAM Algorithms Based on a Graph of Relations
Burgard, W.; Stachniss, C.; Grisetti, G.; Steder, B.; Kümmerle, R.; Dornhege, C.; Ruhnke, M.; Kleiner, Alexander; Tardós, Juan D.
2009-01-01
In this paper, we address the problem of creating an objective benchmark for comparing SLAM approaches. We propose a framework for analyzing the results of SLAM approaches based on a metric for measuring the error of the corrected trajectory. The metric uses only relative relations between poses and does not rely on a global reference frame. The idea is related to graph-based SLAM approaches, namely to consider the energy that is needed to deform the trajectory estimated by a SLAM approach in...
Jing Chen
2015-01-01
This study takes the concept of food logistics distribution as the breakthrough point, by means of the aim of optimization of food logistics distribution routes and analysis of the optimization model of food logistics route, as well as the interpretation of the genetic algorithm, it discusses the optimization of food logistics distribution route based on genetic and cluster scheme algorithm.
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
An improved recommended algorithm for network structure based on two partial graphs
Directory of Open Access Journals (Sweden)
Deng Song
2017-08-01
Full Text Available In this thesis,we introduce an improved algorithm based on network structure.Based on the standard material diffusion algorithm,considering the influence of the user's score on the recommendation,the adjustment factor of the initial resource allocation vector and the resource transfer matrix in the recommendation algorithm is improved.Using the practical data set from GroupLens webite to evaluate the performance of the proposed algorithm,we performed a series of experiments.The experimental results reveal that it can yield better recommendation accuracy and has higher hitting rate than collaborative filtering,network-based inference.It can solve the problem of cold start and scalability in the standard material diffusion algorithm.And it also can make the recommendation results diversified.
Liu, Yuelu; Hong, Xiangfei; Bengson, Jesse J; Kelley, Todd A; Ding, Mingzhou; Mangun, George R
2017-08-15
The neural mechanisms by which intentions are transformed into actions remain poorly understood. We investigated the network mechanisms underlying spontaneous voluntary decisions about where to focus visual-spatial attention (willed attention). Graph-theoretic analysis of two independent datasets revealed that regions activated during willed attention form a set of functionally-distinct networks corresponding to the frontoparietal network, the cingulo-opercular network, and the dorsal attention network. Contrasting willed attention with instructed attention (where attention is directed by external cues), we observed that the dorsal anterior cingulate cortex was allied with the dorsal attention network in instructed attention, but shifted connectivity during willed attention to interact with the cingulo-opercular network, which then mediated communications between the frontoparietal network and the dorsal attention network. Behaviorally, greater connectivity in network hubs, including the dorsolateral prefrontal cortex, the dorsal anterior cingulate cortex, and the inferior parietal lobule, was associated with faster reaction times. These results, shown to be consistent across the two independent datasets, uncover the dynamic organization of functionally-distinct networks engaged to support intentional acts. Copyright © 2017 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Wang, Jieqiong; Li, Ting; Xian, Junfang; Wang, Ningli; He, Huiguang
2016-01-01
Most previous glaucoma studies with resting-state fMRI have focused on the neuronal activity in the individual structure of the brain, yet ignored the functional communication of anatomically separated structures. The purpose of this study is to investigate the efficiency of the functional communication change or not in glaucoma patients. We applied the resting-state fMRI data to construct the connectivity network of 25 normal controls and 25 age-gender-matched primary open angle glaucoma patients. Graph theoretical analysis was performed to assess brain network pattern differences between the two groups. No significant differences of the global network measures were found between the two groups. However, the local measures were radically reorganized in glaucoma patients. Comparing with the hub regions in normal controls' network, we found that six hub regions disappeared and nine hub regions appeared in the network of patients. In addition, the betweenness centralities of two altered hub regions, right fusiform gyrus and right lingual gyrus, were significantly correlated with the visual field mean deviation. Although the efficiency of functional communication is preserved in the brain network of the glaucoma at the global level, the efficiency of functional communication is altered in some specialized regions of the glaucoma. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Wang, Jieqiong [Chinese Academy of Sciences, State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Beijing (China); Li, Ting; Xian, Junfang [Capital Medical University, Department of Radiology, Beijing Tongren Hospital, Beijing (China); Wang, Ningli [Capital Medical University, Department of Ophthalmology, Beijing Tongren Hospital, Beijing (China); He, Huiguang [Chinese Academy of Sciences, State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Beijing (China); Chinese Academy of Sciences, Research Center for Brain-Inspired Intelligence, Institute of Automation, Beijing (China)
2016-11-15
Most previous glaucoma studies with resting-state fMRI have focused on the neuronal activity in the individual structure of the brain, yet ignored the functional communication of anatomically separated structures. The purpose of this study is to investigate the efficiency of the functional communication change or not in glaucoma patients. We applied the resting-state fMRI data to construct the connectivity network of 25 normal controls and 25 age-gender-matched primary open angle glaucoma patients. Graph theoretical analysis was performed to assess brain network pattern differences between the two groups. No significant differences of the global network measures were found between the two groups. However, the local measures were radically reorganized in glaucoma patients. Comparing with the hub regions in normal controls' network, we found that six hub regions disappeared and nine hub regions appeared in the network of patients. In addition, the betweenness centralities of two altered hub regions, right fusiform gyrus and right lingual gyrus, were significantly correlated with the visual field mean deviation. Although the efficiency of functional communication is preserved in the brain network of the glaucoma at the global level, the efficiency of functional communication is altered in some specialized regions of the glaucoma. (orig.)
Ye, Zheng; Doñamayor, Nuria; Münte, Thomas F
2014-02-01
A set of cortical and sub-cortical brain structures has been linked with sentence-level semantic processes. However, it remains unclear how these brain regions are organized to support the semantic integration of a word into sentential context. To look into this issue, we conducted a functional magnetic resonance imaging (fMRI) study that required participants to silently read sentences with semantically congruent or incongruent endings and analyzed the network properties of the brain with two approaches, independent component analysis (ICA) and graph theoretical analysis (GTA). The GTA suggested that the whole-brain network is topologically stable across conditions. The ICA revealed a network comprising the supplementary motor area (SMA), left inferior frontal gyrus, left middle temporal gyrus, left caudate nucleus, and left angular gyrus, which was modulated by the incongruity of sentence ending. Furthermore, the GTA specified that the connections between the left SMA and left caudate nucleus as well as that between the left caudate nucleus and right thalamus were stronger in response to incongruent vs. congruent endings. Copyright © 2012 Wiley Periodicals, Inc.
Quantitative graph theory mathematical foundations and applications
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
The Algorithm Theoretical Basis Document for Level 1A Processing
Jester, Peggy L.; Hancock, David W., III
2012-01-01
The first process of the Geoscience Laser Altimeter System (GLAS) Science Algorithm Software converts the Level 0 data into the Level 1A Data Products. The Level 1A Data Products are the time ordered instrument data converted from counts to engineering units. This document defines the equations that convert the raw instrument data into engineering units. Required scale factors, bias values, and coefficients are defined in this document. Additionally, required quality assurance and browse products are defined in this document.
Sensor and ad-hoc networks theoretical and algorithmic aspects
Makki, S Kami; Pissinou, Niki; Makki, Shamila; Karimi, Masoumeh; Makki, Kia
2008-01-01
This book brings together leading researchers and developers in the field of wireless sensor networks to explain the special problems and challenges of the algorithmic aspects of sensor and ad-hoc networks. The book also fosters communication not only between the different sensor and ad-hoc communities, but also between those communities and the distributed systems and information systems communities. The topics addressed pertain to the sensors and mobile environment.
Theoretical algorithms for satellite-derived sea surface temperatures
Barton, I. J.; Zavody, A. M.; O'Brien, D. M.; Cutten, D. R.; Saunders, R. W.; Llewellyn-Jones, D. T.
1989-03-01
Reliable climate forecasting using numerical models of the ocean-atmosphere system requires accurate data sets of sea surface temperature (SST) and surface wind stress. Global sets of these data will be supplied by the instruments to fly on the ERS 1 satellite in 1990. One of these instruments, the Along-Track Scanning Radiometer (ATSR), has been specifically designed to provide SST in cloud-free areas with an accuracy of 0.3 K. The expected capabilities of the ATSR can be assessed using transmission models of infrared radiative transfer through the atmosphere. The performances of several different models are compared by estimating the infrared brightness temperatures measured by the NOAA 9 AVHRR for three standard atmospheres. Of these, a computationally quick spectral band model is used to derive typical AVHRR and ATSR SST algorithms in the form of linear equations. These algorithms show that a low-noise 3.7-μm channel is required to give the best satellite-derived SST and that the design accuracy of the ATSR is likely to be achievable. The inclusion of extra water vapor information in the analysis did not improve the accuracy of multiwavelength SST algorithms, but some improvement was noted with the multiangle technique. Further modeling is required with atmospheric data that include both aerosol variations and abnormal vertical profiles of water vapor and temperature.
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
Information theoretic methods for image processing algorithm optimization
Prokushkin, Sergey F.; Galil, Erez
2015-01-01
Modern image processing pipelines (e.g., those used in digital cameras) are full of advanced, highly adaptive filters that often have a large number of tunable parameters (sometimes > 100). This makes the calibration procedure for these filters very complex, and the optimal results barely achievable in the manual calibration; thus an automated approach is a must. We will discuss an information theory based metric for evaluation of algorithm adaptive characteristics ("adaptivity criterion") using noise reduction algorithms as an example. The method allows finding an "orthogonal decomposition" of the filter parameter space into the "filter adaptivity" and "filter strength" directions. This metric can be used as a cost function in automatic filter optimization. Since it is a measure of a physical "information restoration" rather than perceived image quality, it helps to reduce the set of the filter parameters to a smaller subset that is easier for a human operator to tune and achieve a better subjective image quality. With appropriate adjustments, the criterion can be used for assessment of the whole imaging system (sensor plus post-processing).
The STAPL Parallel Graph Library
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.
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.
A variable-depth search algorithm for recursive bi-partitioning of signal flow graphs
de Kock, E.A.; Aarts, E.H.L.; Essink, G.; Jansen, R.E.J.; Korst, J.H.M.
1995-01-01
We discuss the use of local search techniques for mapping video algorithms onto programmable high-performance video signal processors. The mapping problem is very complex due to many constraints that need to be satisfied in order to obtain a feasible solution. The complexity is reduced by
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...
Directory of Open Access Journals (Sweden)
Daniil S. Chivilikhin
2014-11-01
Full Text Available The procedure of testing traditionally used in software engineering cannot guarantee program correctness; therefore verification is used at the excess requirements to programs reliability. Verification makes it possible to check certain properties of programs in all possible computational states; however, this process is very complex. In the model checking method a model of the program is built (often, manually and requirements in terms of temporal logic are formulated. Such temporal properties of the model can be checked automatically. The main issue in this framework is the gap between the program and its model. Automata-based programming paradigm gives the possibility to overcome this limitation. In this paradigm, program logic is represented using finite-state machines. The advantage of finite-state machines is that their models can be constructed automatically. The paper deals with the application of mutation-based ant colony optimization algorithm to the problem of finite-state machine construction from their specification, defined by test scenarios and temporal properties. The presented approach has been tested on the elevator doors control problem as well as on randomly generated data. Obtained results show the ant colony algorithm is two-three times faster than the previously used genetic algorithm. The proposed approach can be recommended for inferring control programs for critical systems.
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.
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.
Graphing trillions of triangles.
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.
Multiway simple cycle separators and I/O-efficient algorithms for planar graphs
DEFF Research Database (Denmark)
Arge, L.; Walderveen, Freek van; Zeh, Norbert
2013-01-01
memory, where sort(N) is the number of I/Os needed to sort N items in external memory. The key, and the main technical contribution of this paper, is a multiway version of Miller's simple cycle separator theorem. We show how to compute these separators in linear time in internal memory, and using O...... in internal memory, thereby completely negating the performance gain achieved by minimizing the number of disk accesses. In this paper, we show how to make these algorithms simultaneously efficient in internal and external memory so they achieve I/O complexity O(sort(N)) and take O(N log N) time in internal......(sort(N)) I/Os and O(N log N) (internal-memory computation) time in external memory....
Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm
Liang, Yufeng; Prendergast, David
2018-05-01
The growing interest in using x-ray spectroscopy for refined materials characterization calls for an accurate electronic-structure theory to interpret the x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a nondiagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017), 10.1103/PhysRevLett.118.096402], we exploit the linear dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of vanishingly small terms. This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path-finding process. We demonstrate that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.
Jacomy, Mathieu; Venturini, Tommaso; Heymann, Sebastien; Bastian, Mathieu
2014-01-01
Gephi is a network visualization software used in various disciplines (social network analysis, biology, genomics...). One of its key features is the ability to display the spatialization process, aiming at transforming the network into a map, and ForceAtlas2 is its default layout algorithm. The latter is developed by the Gephi team as an all-around solution to Gephi users' typical networks (scale-free, 10 to 10,000 nodes). We present here for the first time its functioning and settings. ForceAtlas2 is a force-directed layout close to other algorithms used for network spatialization. We do not claim a theoretical advance but an attempt to integrate different techniques such as the Barnes Hut simulation, degree-dependent repulsive force, and local and global adaptive temperatures. It is designed for the Gephi user experience (it is a continuous algorithm), and we explain which constraints it implies. The algorithm benefits from much feedback and is developed in order to provide many possibilities through its settings. We lay out its complete functioning for the users who need a precise understanding of its behaviour, from the formulas to graphic illustration of the result. We propose a benchmark for our compromise between performance and quality. We also explain why we integrated its various features and discuss our design choices.
The STAPL Parallel Graph Library
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
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.
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.
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.
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%.
Interactive Graph Layout of a Million Nodes
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...
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
Cao, Hengyi; Plichta, Michael M; Schäfer, Axel; Haddad, Leila; Grimm, Oliver; Schneider, Michael; Esslinger, Christine; Kirsch, Peter; Meyer-Lindenberg, Andreas; Tost, Heike
2014-01-01
The investigation of the brain connectome with functional magnetic resonance imaging (fMRI) and graph theory analyses has recently gained much popularity, but little is known about the robustness of these properties, in particular those derived from active fMRI tasks. Here, we studied the test-retest reliability of brain graphs calculated from 26 healthy participants with three established fMRI experiments (n-back working memory, emotional face-matching, resting state) and two parcellation schemes for node definition (AAL atlas, functional atlas proposed by Power et al.). We compared the intra-class correlation coefficients (ICCs) of five different data processing strategies and demonstrated a superior reliability of task-regression methods with condition-specific regressors. The between-task comparison revealed significantly higher ICCs for resting state relative to the active tasks, and a superiority of the n-back task relative to the face-matching task for global and local network properties. While the mean ICCs were typically lower for the active tasks, overall fair to good reliabilities were detected for global and local connectivity properties, and for the n-back task with both atlases, smallworldness. For all three tasks and atlases, low mean ICCs were seen for the local network properties. However, node-specific good reliabilities were detected for node degree in regions known to be critical for the challenged functions (resting-state: default-mode network nodes, n-back: fronto-parietal nodes, face-matching: limbic nodes). Between-atlas comparison demonstrated significantly higher reliabilities for the functional parcellations for global and local network properties. Our findings can inform the choice of processing strategies, brain atlases and outcome properties for fMRI studies using active tasks, graph theory methods, and within-subject designs, in particular future pharmaco-fMRI studies. © 2013 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Longquan Yong
2012-01-01
Full Text Available Harmony search (HS method is an emerging metaheuristic optimization algorithm. In this paper, an improved harmony search method based on differential mutation operator (IHSDE is proposed to deal with the optimization problems. Since the population diversity plays an important role in the behavior of evolution algorithm, the aim of this paper is to calculate the expected population mean and variance of IHSDE from theoretical viewpoint. Numerical results, compared with the HSDE, NGHS, show that the IHSDE method has good convergence property over a test-suite of well-known benchmark functions.
Hively, Lee M.
2014-09-16
Data collected from devices and human condition may be used to forewarn of critical events such as machine/structural failure or events from brain/heart wave data stroke. By monitoring the data, and determining what values are indicative of a failure forewarning, one can provide adequate notice of the impending failure in order to take preventive measures. This disclosure teaches a computer-based method to convert dynamical numeric data representing physical objects (unstructured data) into discrete-phase-space states, and hence into a graph (structured data) for extraction of condition change.
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
Vecchio, Fabrizio; Di Iorio, Riccardo; Miraglia, Francesca; Granata, Giuseppe; Romanello, Roberto; Bramanti, Placido; Rossini, Paolo Maria
2018-04-01
Transcranial direct current stimulation (tDCS) is a non-invasive technique able to modulate cortical excitability in a polarity-dependent way. At present, only few studies investigated the effects of tDCS on the modulation of functional connectivity between remote cortical areas. The aim of this study was to investigate-through graph theory analysis-how bipolar tDCS modulate cortical networks high-density EEG recordings were acquired before and after bipolar cathodal, anodal and sham tDCS involving the primary motor and pre-motor cortices of the dominant hemispherein 14 healthy subjects. Results showed that, after bipolar anodal tDCS stimulation, brain networks presented a less evident "small world" organization with a global tendency to be more random in its functional connections with respect to prestimulus condition in both hemispheres. Results suggest that tDCS globally modulates the cortical connectivity of the brain, modifying the underlying functional organization of the stimulated networks, which might be related to changes in synaptic efficiency of the motor network and related brain areas. This study demonstrated that graph analysis approach to EEG recordings is able to intercept changes in cortical functions mediated by bipolar anodal tDCS mainly involving the dominant M1 and related motor areas. Concluding, tDCS could be an useful technique to help understanding brain rhythms and their topographic functional organization and specificity.
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...
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...
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.
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)
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.
Groupies in multitype random graphs
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.
Groupies in multitype random graphs.
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.
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.
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.
Park, Bong Soo; Lee, Yoo Jin; Park, Jin-Han; Kim, Il Hwan; Park, Si Hyung; Lee, Ho-Joon; Park, Kang Min
2018-06-01
We evaluated global topology and organization of regional hubs in the brain networks and microstructural abnormalities in the white matter of patients with reflex syncope. Twenty patients with reflex syncope and thirty healthy subjects were recruited, and they underwent diffusion tensor imaging (DTI) scans. Graph theory was applied to obtain network measures based on extracted DTI data, using DSI Studio. We then investigated differences in the network measures between the patients with reflex syncope and the healthy subjects. We also analyzed microstructural abnormalities of white matter using tract-based spatial statistics analysis (TBSS). Measures of global topology were not different between patients with reflex syncope and healthy subjects. However, in reflex syncope patients, the strength measures of the right angular, left inferior frontal, left middle orbitofrontal, left superior medial frontal, and left middle temporal gyrus were lower than in healthy subjects. The betweenness centrality measures of the left middle orbitofrontal, left fusiform, and left lingual gyrus in patients were lower than those in healthy subjects. The PageRank centrality measures of the right angular, left middle orbitofrontal, and left superior medial frontal gyrus in patients were lower than those in healthy subjects. Regarding the analysis of the white matter microstructure, there were no differences in the fractional anisotropy and mean diffusivity values between the two groups. We have identified a reorganization of network hubs in the brain network of patients with reflex syncope. These alterations in brain network may play a role in the pathophysiologic mechanism underlying reflex syncope. © 2018 The Authors. Brain and Behavior published by Wiley Periodicals, Inc.
A faithful functor among algebras and graphs
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.
Graphs with branchwidth at most three
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
Constructing Dense Graphs with Unique Hamiltonian Cycles
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…
Information Retrieval and Graph Analysis Approaches for Book Recommendation
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 ...
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.
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
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
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
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.; Dominguez, Luis; Panos, Christos; Kouramas, Konstantinos; Chinchuluun, Altannar
2012-01-01
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.
2012-04-21
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
DEFF Research Database (Denmark)
Oxvig, Christian Schou; Pedersen, Patrick Steffen; Arildsen, Thomas
2013-01-01
Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed ℓ0 norm reconstruction...... algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for fixed quality and required time. In this paper, we present simulation results that show a phase transition surpassing that of the theoretical ℓ1 approach......: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time....
Research on network maximum flows algorithm of cascade level graph%级连层次图的网络最大流算法研究
Institute of Scientific and Technical Information of China (English)
潘荷新; 伊崇信; 李满
2011-01-01
给出一种通过构造网络级连层次图的方法,来间接求出最大网络流的算法.对于给定的有n个顶点,P条边的网络N=(G,s,t,C),该算法可在O(n2)时间内快速求出流经网络N的最大网络流及达最大流时的网络流.%This paper gives an algoritm that structures a network cascade level graph to find out maximum flow of the network indirectly.For the given network N=(G,s,t,C) that has n vetexes and e arcs,this algorithm finds out the maximum value of the network flow fast in O(n2) time that flows from the network N and the network flows when the value of the one reach maximum.
完全图的点可区别强全染色算法%Strong Vertex-distinguishing Total Coloring Algorithm of Complete Graph
Institute of Scientific and Technical Information of China (English)
赵焕平; 刘平; 李敬文
2012-01-01
According to the definition of strong vertex-distinguishing total coloring, this paper combines with the symmetry of complete graph, proposes a new strong vertex-distinguishing total coloring algorithm. The algorithm divides the filled colors into two parts: overcolor and propercolor. At the premise of getting the coloring number and the coloring frequency, it uses colored at first to enhance its convergence. Experimental results show that this algorithm has a lower time complexity.%根据图的点可区别全染色的定义,结合完全图的对称性,提出一种新的点可区别强全染色算法.该算法将需要填充的颜色分为超色数和正常色数2个部分,在得到染色数量和染色次数的前提下,对超色数进行染色以增强算法收敛性.实验结果表明,该算法具有较低的时间复杂度.
An algorithm for hyperspectral remote sensing of aerosols: 1. Development of theoretical framework
International Nuclear Information System (INIS)
Hou, Weizhen; Wang, Jun; Xu, Xiaoguang; Reid, Jeffrey S.; Han, Dong
2016-01-01
This paper describes the first part of a series of investigations to develop algorithms for simultaneous retrieval of aerosol parameters and surface reflectance from a newly developed hyperspectral instrument, the GEOstationary Trace gas and Aerosol Sensor Optimization (GEO-TASO), by taking full advantage of available hyperspectral measurement information in the visible bands. We describe the theoretical framework of an inversion algorithm for the hyperspectral remote sensing of the aerosol optical properties, in which major principal components (PCs) for surface reflectance is assumed known, and the spectrally dependent aerosol refractive indices are assumed to follow a power-law approximation with four unknown parameters (two for real and two for imaginary part of refractive index). New capabilities for computing the Jacobians of four Stokes parameters of reflected solar radiation at the top of the atmosphere with respect to these unknown aerosol parameters and the weighting coefficients for each PC of surface reflectance are added into the UNified Linearized Vector Radiative Transfer Model (UNL-VRTM), which in turn facilitates the optimization in the inversion process. Theoretical derivations of the formulas for these new capabilities are provided, and the analytical solutions of Jacobians are validated against the finite-difference calculations with relative error less than 0.2%. Finally, self-consistency check of the inversion algorithm is conducted for the idealized green-vegetation and rangeland surfaces that were spectrally characterized by the U.S. Geological Survey digital spectral library. It shows that the first six PCs can yield the reconstruction of spectral surface reflectance with errors less than 1%. Assuming that aerosol properties can be accurately characterized, the inversion yields a retrieval of hyperspectral surface reflectance with an uncertainty of 2% (and root-mean-square error of less than 0.003), which suggests self-consistency in the
Nagasinghe, Iranga
2010-01-01
This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…
Goldengorin, Boris; Vink, Marius de
1999-01-01
The Data-Correcting Algorithm (DCA) corrects the data of a hard problem instance in such a way that we obtain an instance of a well solvable special case. For a given prescribed accuracy of the solution, the DCA uses a branch and bound scheme to make sure that the solution of the corrected instance
Graph Sampling for Covariance Estimation
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
Graph Sampling for Covariance Estimation
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.
Boersma, Maria; Smit, Dirk J A; Boomsma, Dorret I; De Geus, Eco J C; Delemarre-van de Waal, Henriette A; Stam, Cornelis J
2013-01-01
The child brain is a small-world network, which is hypothesized to change toward more ordered configurations with development. In graph theoretical studies, comparing network topologies under different conditions remains a critical point. Constructing a minimum spanning tree (MST) might present a solution, since it does not require setting a threshold and uses a fixed number of nodes and edges. In this study, the MST method is introduced to examine developmental changes in functional brain network topology in young children. Resting-state electroencephalography was recorded from 227 children twice at 5 and 7 years of age. Synchronization likelihood (SL) weighted matrices were calculated in three different frequency bands from which MSTs were constructed, which represent constructs of the most important routes for information flow in a network. From these trees, several parameters were calculated to characterize developmental change in network organization. The MST diameter and eccentricity significantly increased, while the leaf number and hierarchy significantly decreased in the alpha band with development. Boys showed significant higher leaf number, betweenness, degree and hierarchy and significant lower SL, diameter, and eccentricity than girls in the theta band. The developmental changes indicate a shift toward more decentralized line-like trees, which supports the previously hypothesized increase toward regularity of brain networks with development. Additionally, girls showed more line-like decentralized configurations, which is consistent with the view that girls are ahead of boys in brain development. MST provides an elegant method sensitive to capture subtle developmental changes in network organization without the bias of network comparison.
DEFF Research Database (Denmark)
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Line-based monocular graph SLAM algorithm%基于图优化的单目线特征SLAM算法
Institute of Scientific and Technical Information of China (English)
董蕊芳; 柳长安; 杨国田; 程瑞营
2017-01-01
A new line based 6-DOF monocular algorithm for using graph simultaneous localization and mapping(SLAM) algoritm was proposed.First,the straight line were applied as a feature instead of points,due to a map consisting of a sparse set of 3D points is unable to describe the structure of the surrounding world.Secondly,most of previous line-based SLAM algorithms were focused on filtering-based solutions suffering from the inconsistent when applied to the inherently non-linear SLAM problem,in contrast,the graph-based solution was used to improve the accuracy of the localization and the consistency of mapping.Thirdly,a special line representation was exploited for combining the Plücker coordinates with the Cayley representation.The Plücker coordinates were used for the 3D line projection function,and the Cayley representation helps to update the line parameters during the non-linear optimization process.Finally,the simulation experiment shows that the proposed algorithm outperforms odometry and EKF-based SLAM in terms of the pose estimation,while the sum of the squared errors (SSE) and root-mean-square error (RMSE) of proposed method are 2.5％ and 10.5％ of odometry,and 22.4％ and 33％ of EKF-based SLAM.The reprojection error is only 45.5 pixels.The real image experiment shows that the proposed algorithm obtains only 958 cm2 and 3.941 3 cm the SSE and RMSE of pose estimation.Therefore,it can be concluded that the proposed algorithm is effective and accuracy.%提出了基于图优化的单目线特征同时定位和地图构建(SLAM)的方法.首先,针对主流视觉SLAM算法因采用点作为特征而导致构建的点云地图稀疏、难以准确表达环境结构信息等缺点,采用直线作为特征来构建地图.然后,根据现有线特征的SLAM算法都是基于滤波器的SLAM框架、存在线性化及更新效率的问题,采用基于图优化的SLAM解决方案以提高定位精度及地图构建的一致性和准确性.将线特征的Plücker坐
Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions
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].
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.
Information Retrieval and Graph Analysis Approaches for Book Recommendation.
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.
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.
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
Huang, Chien-Hung; Chang, Peter Mu-Hsin; Hsu, Chia-Wei; Huang, Chi-Ying F; Ng, Ka-Lok
2016-01-11
Non-small cell lung cancer (NSCLC) is one of the leading causes of death globally, and research into NSCLC has been accumulating steadily over several years. Drug repositioning is the current trend in the pharmaceutical industry for identifying potential new uses for existing drugs and accelerating the development process of drugs, as well as reducing side effects. This work integrates two approaches--machine learning algorithms and topological parameter-based classification--to develop a novel pipeline of drug repositioning to analyze four lung cancer microarray datasets, enriched biological processes, potential therapeutic drugs and targeted genes for NSCLC treatments. A total of 7 (8) and 11 (12) promising drugs (targeted genes) were discovered for treating early- and late-stage NSCLC, respectively. The effectiveness of these drugs is supported by the literature, experimentally determined in-vitro IC50 and clinical trials. This work provides better drug prediction accuracy than competitive research according to IC50 measurements. With the novel pipeline of drug repositioning, the discovery of enriched pathways and potential drugs related to NSCLC can provide insight into the key regulators of tumorigenesis and the treatment of NSCLC. Based on the verified effectiveness of the targeted drugs predicted by this pipeline, we suggest that our drug-finding pipeline is effective for repositioning drugs.
Multiple graph regularized protein domain ranking
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.
Multiple graph regularized protein domain ranking
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.
Multiple graph regularized protein domain ranking.
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.
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.
A new fast algorithm for computing a complex number: Theoretic transforms
Reed, I. S.; Liu, K. Y.; Truong, T. K.
1977-01-01
A high-radix fast Fourier transformation (FFT) algorithm for computing transforms over GF(sq q), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
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.
van Otterlo, Martijn
2017-01-01
Ethics of algorithms is an emerging topic in various disciplines such as social science, law, and philosophy, but also artificial intelligence (AI). The value alignment problem expresses the challenge of (machine) learning values that are, in some way, aligned with human requirements or values. In this paper I argue for looking at how humans have formalized and communicated values, in professional codes of ethics, and for exploring declarative decision-theoretic ethical programs (DDTEP) to fo...
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.
Stability notions in synthetic graph generation: a preliminary study
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,
On the Recognition of Fuzzy Circular Interval Graphs
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.
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.
Graph embedding with rich information through heterogeneous graph
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.
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Graph theory and its applications
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.
Towards a theory of geometric graphs
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...
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
Subsampling for graph power spectrum estimation
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.
Subsampling for graph power spectrum estimation
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.
Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco
2012-11-01
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating
Indian Academy of Sciences (India)
polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.
The Container Problem in Bubble-Sort Graphs
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.
Mohanty, Rakesh; Sharma, Burle; Tripathy, Sasmita
2011-01-01
List Accessing Problem is a well studied research problem in the context of linear search. Input to the list accessing problem is an unsorted linear list of distinct elements along with a sequence of requests, where each request is an access operation on an element of the list. A list accessing algorithm reorganizes the list while processing a request sequence on the list in order to minimize the access cost. Move-To-Front algorithm has been proved to be the best performing list accessing onl...
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Performance criteria for graph clustering and Markov cluster experiments
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
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)
Network reconstruction via graph blending
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.
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.
A game theoretic algorithm to detect overlapping community structure in networks
Zhou, Xu; Zhao, Xiaohui; Liu, Yanheng; Sun, Geng
2018-04-01
Community detection can be used as an important technique for product and personalized service recommendation. A game theory based approach to detect overlapping community structure is introduced in this paper. The process of the community formation is converted into a game, when all agents (nodes) cannot improve their own utility, the game process will be terminated. The utility function is composed of a gain and a loss function and we present a new gain function in this paper. In addition, different from choosing action randomly among join, quit and switch for each agent to get new label, two new strategies for each agent to update its label are designed during the game, and the strategies are also evaluated and compared for each agent in order to find its best result. The overlapping community structure is naturally presented when the stop criterion is satisfied. The experimental results demonstrate that the proposed algorithm outperforms other similar algorithms for detecting overlapping communities in networks.
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Simplifying Scalable Graph Processing with a Domain-Specific Language
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.
Simplifying Scalable Graph Processing with a Domain-Specific Language
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.
Wang, Jin-Hui; Zuo, Xi-Nian; Gohel, Suril; Milham, Michael P.; Biswal, Bharat B.; He, Yong
2011-01-01
Graph-based computational network analysis has proven a powerful tool to quantitatively characterize functional architectures of the brain. However, the test-retest (TRT) reliability of graph metrics of functional networks has not been systematically examined. Here, we investigated TRT reliability of topological metrics of functional brain networks derived from resting-state functional magnetic resonance imaging data. Specifically, we evaluated both short-term (5 months apart) TRT reliability for 12 global and 6 local nodal network metrics. We found that reliability of global network metrics was overall low, threshold-sensitive and dependent on several factors of scanning time interval (TI, long-term>short-term), network membership (NM, networks excluding negative correlations>networks including negative correlations) and network type (NT, binarized networks>weighted networks). The dependence was modulated by another factor of node definition (ND) strategy. The local nodal reliability exhibited large variability across nodal metrics and a spatially heterogeneous distribution. Nodal degree was the most reliable metric and varied the least across the factors above. Hub regions in association and limbic/paralimbic cortices showed moderate TRT reliability. Importantly, nodal reliability was robust to above-mentioned four factors. Simulation analysis revealed that global network metrics were extremely sensitive (but varying degrees) to noise in functional connectivity and weighted networks generated numerically more reliable results in compared with binarized networks. For nodal network metrics, they showed high resistance to noise in functional connectivity and no NT related differences were found in the resistance. These findings provide important implications on how to choose reliable analytical schemes and network metrics of interest. PMID:21818285
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.
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.
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.
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.
Indian Academy of Sciences (India)
to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...
Blind information-theoretic multiuser detection algorithms for DS-CDMA and WCDMA downlink systems.
Waheed, Khuram; Salem, Fathi M
2005-07-01
Code division multiple access (CDMA) is based on the spread-spectrum technology and is a dominant air interface for 2.5G, 3G, and future wireless networks. For the CDMA downlink, the transmitted CDMA signals from the base station (BS) propagate through a noisy multipath fading communication channel before arriving at the receiver of the user equipment/mobile station (UE/MS). Classical CDMA single-user detection (SUD) algorithms implemented in the UE/MS receiver do not provide the required performance for modern high data-rate applications. In contrast, multi-user detection (MUD) approaches require a lot of a priori information not available to the UE/MS. In this paper, three promising adaptive Riemannian contra-variant (or natural) gradient based user detection approaches, capable of handling the highly dynamic wireless environments, are proposed. The first approach, blind multiuser detection (BMUD), is the process of simultaneously estimating multiple symbol sequences associated with all the users in the downlink of a CDMA communication system using only the received wireless data and without any knowledge of the user spreading codes. This approach is applicable to CDMA systems with relatively short spreading codes but becomes impractical for systems using long spreading codes. We also propose two other adaptive approaches, namely, RAKE -blind source recovery (RAKE-BSR) and RAKE-principal component analysis (RAKE-PCA) that fuse an adaptive stage into a standard RAKE receiver. This adaptation results in robust user detection algorithms with performance exceeding the linear minimum mean squared error (LMMSE) detectors for both Direct Sequence CDMA (DS-CDMA) and wide-band CDMA (WCDMA) systems under conditions of congestion, imprecise channel estimation and unmodeled multiple access interference (MAI).
Pezzotti, Giuseppe; Zhu, Wenliang; Boffelli, Marco; Adachi, Tetsuya; Ichioka, Hiroaki; Yamamoto, Toshiro; Marunaka, Yoshinori; Kanamura, Narisato
2015-05-01
The Raman spectroscopic method has quantitatively been applied to the analysis of local crystallographic orientation in both single-crystal hydroxyapatite and human teeth. Raman selection rules for all the vibrational modes of the hexagonal structure were expanded into explicit functions of Euler angles in space and six Raman tensor elements (RTE). A theoretical treatment has also been put forward according to the orientation distribution function (ODF) formalism, which allows one to resolve the statistical orientation patterns of the nm-sized hydroxyapatite crystallite comprised in the Raman microprobe. Close-form solutions could be obtained for the Euler angles and their statistical distributions resolved with respect to the direction of the average texture axis. Polarized Raman spectra from single-crystalline hydroxyapatite and textured polycrystalline (teeth enamel) samples were compared, and a validation of the proposed Raman method could be obtained through confirming the agreement between RTE values obtained from different samples.
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...
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.
Quick Mining of Isomorphic Exact Large Patterns from Large Graphs
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.
Quick Mining of Isomorphic Exact Large Patterns from Large Graphs
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.
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...
Planning additional drilling campaign using two-space genetic algorithm: A game theoretical approach
Kumral, Mustafa; Ozer, Umit
2013-03-01
Grade and tonnage are the most important technical uncertainties in mining ventures because of the use of estimations/simulations, which are mostly generated from drill data. Open pit mines are planned and designed on the basis of the blocks representing the entire orebody. Each block has different estimation/simulation variance reflecting uncertainty to some extent. The estimation/simulation realizations are submitted to mine production scheduling process. However, the use of a block model with varying estimation/simulation variances will lead to serious risk in the scheduling. In the medium of multiple simulations, the dispersion variances of blocks can be thought to regard technical uncertainties. However, the dispersion variance cannot handle uncertainty associated with varying estimation/simulation variances of blocks. This paper proposes an approach that generates the configuration of the best additional drilling campaign to generate more homogenous estimation/simulation variances of blocks. In other words, the objective is to find the best drilling configuration in such a way as to minimize grade uncertainty under budget constraint. Uncertainty measure of the optimization process in this paper is interpolation variance, which considers data locations and grades. The problem is expressed as a minmax problem, which focuses on finding the best worst-case performance i.e., minimizing interpolation variance of the block generating maximum interpolation variance. Since the optimization model requires computing the interpolation variances of blocks being simulated/estimated in each iteration, the problem cannot be solved by standard optimization tools. This motivates to use two-space genetic algorithm (GA) approach to solve the problem. The technique has two spaces: feasible drill hole configuration with minimization of interpolation variance and drill hole simulations with maximization of interpolation variance. Two-space interacts to find a minmax solution
Information-optimal genome assembly via sparse read-overlap graphs.
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.
Bipartite separability and nonlocal quantum operations on graphs
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.
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.
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
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...
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.
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)
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)
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.)
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.)
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.
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.
Low-Rank Matrix Factorization With Adaptive Graph Regularizer.
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.
Indian Academy of Sciences (India)
ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...
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,.
Graph Regularized Auto-Encoders for Image Representation.
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.
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.
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.
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
Indian Academy of Sciences (India)
algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).
Indian Academy of Sciences (India)
algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...
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)
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].
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Zhao, Yongli; Tian, Rui; Yu, Xiaosong; Zhang, Jiawei; Zhang, Jie
2017-03-01
A proper traffic grooming strategy in dynamic optical networks can improve the utilization of bandwidth resources. An auxiliary graph (AG) is designed to solve the traffic grooming problem under a dynamic traffic scenario in spatial division multiplexing enabled elastic optical networks (SDM-EON) with multi-core fibers. Five traffic grooming policies achieved by adjusting the edge weights of an AG are proposed and evaluated through simulation: maximal electrical grooming (MEG), maximal optical grooming (MOG), maximal SDM grooming (MSG), minimize virtual hops (MVH), and minimize physical hops (MPH). Numeric results show that each traffic grooming policy has its own features. Among different traffic grooming policies, an MPH policy can achieve the lowest bandwidth blocking ratio, MEG can save the most transponders, and MSG can obtain the fewest cores for each request.
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.
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.
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.
Indian Academy of Sciences (India)
will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...
EmptyHeaded: A Relational Engine for Graph Processing.
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.
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
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
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.
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].
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
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.
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.
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
Joint Graph Layouts for Visualizing Collections of Segmented Meshes
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.
Joint Graph Layouts for Visualizing Collections of Segmented Meshes
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.
Directory of Open Access Journals (Sweden)
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
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.
Expander graphs in pure and applied mathematics
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.
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.
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...
A NEW HYBRID GENETIC ALGORITHM FOR VERTEX COVER PROBLEM
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...
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.
Large-Scale Graph Processing Using Apache Giraph
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.
Large-Scale Graph Processing Using Apache Giraph
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.
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.
International Nuclear Information System (INIS)
Sitko, Rafal
2008-01-01
Knowledge of X-ray tube spectral distribution is necessary in theoretical methods of matrix correction, i.e. in both fundamental parameter (FP) methods and theoretical influence coefficient algorithms. Thus, the influence of X-ray tube distribution on the accuracy of the analysis of thin films and bulk samples is presented. The calculations are performed using experimental X-ray tube spectra taken from the literature and theoretical X-ray tube spectra evaluated by three different algorithms proposed by Pella et al. (X-Ray Spectrom. 14 (1985) 125-135), Ebel (X-Ray Spectrom. 28 (1999) 255-266), and Finkelshtein and Pavlova (X-Ray Spectrom. 28 (1999) 27-32). In this study, Fe-Cr-Ni system is selected as an example and the calculations are performed for X-ray tubes commonly applied in X-ray fluorescence analysis (XRF), i.e., Cr, Mo, Rh and W. The influence of X-ray tube spectra on FP analysis is evaluated when quantification is performed using various types of calibration samples. FP analysis of bulk samples is performed using pure-element bulk standards and multielement bulk standards similar to the analyzed material, whereas for FP analysis of thin films, the bulk and thin pure-element standards are used. For the evaluation of the influence of X-ray tube spectra on XRF analysis performed by theoretical influence coefficient methods, two algorithms for bulk samples are selected, i.e. Claisse-Quintin (Can. Spectrosc. 12 (1967) 129-134) and COLA algorithms (G.R. Lachance, Paper Presented at the International Conference on Industrial Inorganic Elemental Analysis, Metz, France, June 3, 1981) and two algorithms (constant and linear coefficients) for thin films recently proposed by Sitko (X-Ray Spectrom. 37 (2008) 265-272)
Multiple graph regularized nonnegative matrix factorization
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.
Graph theoretic aspects of music theory
Althuis, T.A.; Göbel, F.
2001-01-01
The cycle on twelve points is a well-known representation of the twelve pitch classes of the traditional scale. We treat a more general situation where the number of pitch classes can be different from twelve and where, moreover, other measures of closeness are taken into account. We determine all
Systems information management: graph theoretical approach
Temel, T.
2006-01-01
This study proposes a new method for characterising the underlying information structure of a multi-sector system. A complete characterisation is accomplished by identifying information gaps and cause-effect information pathways in the system, and formulating critical testable hypotheses.
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.
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Directory of Open Access Journals (Sweden)
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions
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
Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis
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
Distributed Large Independent Sets in One Round On Bounded-independence Graphs
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...
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
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.
A New Augmentation Based Algorithm for Extracting Maximal Chordal Subgraphs.
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.
High Dimensional Spectral Graph Theory and Non-backtracking Random Walks on Graphs
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.
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
Graph-based semi-supervised learning
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
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...
DEFF Research Database (Denmark)
NJOMO WANDJI, Wilfried
2017-01-01
levels are targeted: existence, location, and severity. The proposed algorithm is analytically developed from the dynamics theory and the virtual energy principle. Some computational techniques are proposed for carrying out computations, including discretization, integration, derivation, and suitable...
Whole Genome Phylogenetic Tree Reconstruction using Colored de Bruijn Graphs
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...
Groups, graphs and random walks
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...
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)
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.
Laplacian Estrada and normalized Laplacian Estrada indices of evolving graphs.
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.
Spectral clustering and biclustering learning large graphs and contingency tables
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
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 ...
Regularities and dynamics in bisimulation reductions of big graphs
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
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....
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...
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
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.
Directory of Open Access Journals (Sweden)
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Energy Technology Data Exchange (ETDEWEB)
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
DEFF Research Database (Denmark)
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Directory of Open Access Journals (Sweden)
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Žuvela, Petar; Liu, J Jay; Macur, Katarzyna; Bączek, Tomasz
2015-10-06
In this work, performance of five nature-inspired optimization algorithms, genetic algorithm (GA), particle swarm optimization (PSO), artificial bee colony (ABC), firefly algorithm (FA), and flower pollination algorithm (FPA), was compared in molecular descriptor selection for development of quantitative structure-retention relationship (QSRR) models for 83 peptides that originate from eight model proteins. The matrix with 423 descriptors was used as input, and QSRR models based on selected descriptors were built using partial least squares (PLS), whereas root mean square error of prediction (RMSEP) was used as a fitness function for their selection. Three performance criteria, prediction accuracy, computational cost, and the number of selected descriptors, were used to evaluate the developed QSRR models. The results show that all five variable selection methods outperform interval PLS (iPLS), sparse PLS (sPLS), and the full PLS model, whereas GA is superior because of its lowest computational cost and higher accuracy (RMSEP of 5.534%) with a smaller number of variables (nine descriptors). The GA-QSRR model was validated initially through Y-randomization. In addition, it was successfully validated with an external testing set out of 102 peptides originating from Bacillus subtilis proteomes (RMSEP of 22.030%). Its applicability domain was defined, from which it was evident that the developed GA-QSRR exhibited strong robustness. All the sources of the model's error were identified, thus allowing for further application of the developed methodology in proteomics.
Handbook of graph drawing and visualization
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
Transduction on Directed Graphs via Absorbing Random Walks.
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.
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...
Minimum nonuniform graph partitioning with unrelated weights
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.
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.
Graph Theory. 1. Fragmentation of Structural Graphs
Directory of Open Access Journals (Sweden)
Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
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.
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.
Directory of Open Access Journals (Sweden)
I. De Smedt
2018-04-01
Full Text Available On board the Copernicus Sentinel-5 Precursor (S5P platform, the TROPOspheric Monitoring Instrument (TROPOMI is a double-channel, nadir-viewing grating spectrometer measuring solar back-scattered earthshine radiances in the ultraviolet, visible, near-infrared, and shortwave infrared with global daily coverage. In the ultraviolet range, its spectral resolution and radiometric performance are equivalent to those of its predecessor OMI, but its horizontal resolution at true nadir is improved by an order of magnitude. This paper introduces the formaldehyde (HCHO tropospheric vertical column retrieval algorithm implemented in the S5P operational processor and comprehensively describes its various retrieval steps. Furthermore, algorithmic improvements developed in the framework of the EU FP7-project QA4ECV are described for future updates of the processor. Detailed error estimates are discussed in the light of Copernicus user requirements and needs for validation are highlighted. Finally, verification results based on the application of the algorithm to OMI measurements are presented, demonstrating the performances expected for TROPOMI.
Carifio, James; Perla, Rocco J.
2009-01-01
This article presents a critical review and analysis of key studies that have been done in science education and other areas on the effects and effectiveness of using diagrams, graphs, photographs, illustrations, and concept maps as "adjunct visual aids" in the learning of scientific-technical content. It also summarizes and reviews those studies…
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Packing Degenerate Graphs Greedily
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
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.
Identifying patients with Alzheimer's disease using resting-state fMRI and graph theory.
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.
A local search for a graph clustering problem
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.
Wu, Jie
2005-01-01
PrefaceAD HOC WIRELESS NETWORKSA Modular Cross Layer Architecture for Ad Hoc Networks, M. Conti, J. Crowcroft, G. Maselli, and G. TuriRouting Scalability in MANETs, J. Eriksson, S. Krishnamurthy and M. FaloutsosUniformly Distributed Algorithm for Virtual Backbone Routing in Ad Hoc Wireless Networks, D.S. KimMaximum Necessary Hop Count for Packet Routing in MANET, X. Chen and J. ShenEfficient Strategyproof Multicast in Selfish Wireless Networks, X.-Yang LiGeocasting in Ad Hoc and Sensor Networks, I. StojmenovicTopology Control for Ad hoc Networks: Present Solutions and Open Issues, C.-C. Shen a
Obozov, A. A.; Serpik, I. N.; Mihalchenko, G. S.; Fedyaeva, G. A.
2017-01-01
In the article, the problem of application of the pattern recognition (a relatively young area of engineering cybernetics) for analysis of complicated technical systems is examined. It is shown that the application of a statistical approach for hard distinguishable situations could be the most effective. The different recognition algorithms are based on Bayes approach, which estimates posteriori probabilities of a certain event and an assumed error. Application of the statistical approach to pattern recognition is possible for solving the problem of technical diagnosis complicated systems and particularly big powered marine diesel engines.
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
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
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...
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
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
Distributed graph coloring fundamentals and recent developments
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
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
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)
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
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
An introduction to grids, graphs, and networks
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
A distributed query execution engine of big attributed graphs.
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.
Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics
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.
Learning molecular energies using localized graph kernels
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.
Directory of Open Access Journals (Sweden)
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Tailored Random Graph Ensembles
International Nuclear Information System (INIS)
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
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.
International Nuclear Information System (INIS)
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
GraphStore: A Distributed Graph Storage System for Big Data Networks
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…
Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions
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
Approximating centrality in evolving graphs: toward sublinearity
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.
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.
A graph model for opportunistic network coding
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.
Three-coloring graphs with no induced seven-vertex path II : using a triangle
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.
Modeling flow and transport in fracture networks using graphs
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
Learning a Nonnegative Sparse Graph for Linear Regression.
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.
Community detection by graph Voronoi diagrams
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.
An algorithm for finding a similar subgraph of all Hamiltonian cycles
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.
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
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.
On some covering graphs of a graph
Directory of Open Access Journals (Sweden)
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
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.
Local search for Steiner tree problems in graphs
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
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.
Applying Graph Theory to Problems in Air Traffic Management
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.
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.
A librarian's guide to graphs, data and the semantic web
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...
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.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
Sampling Large Graphs for Anticipatory Analytics
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
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Subdominant pseudoultrametric on graphs
Energy Technology Data Exchange (ETDEWEB)
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
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)
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.
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.
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
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
On the reachability and observability of path and cycle graphs
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...
Cantor spectra of magnetic chain graphs
Czech Academy of Sciences Publication Activity Database
Exner, Pavel; Vašata, D.
2017-01-01
Roč. 50, č. 16 (2017), č. článku 165201. ISSN 1751-8113 R&D Projects: GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : quantum chain graph * magnetic field * almost Mathieu operator * Cantor spectrum 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) Impact factor: 1.857, year: 2016
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
Using graph approach for managing connectivity in integrative landscape modelling
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
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
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....
Overlapping community detection based on link graph using distance dynamics
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.
Template Generation and Selection Algorithms
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
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
DEFF Research Database (Denmark)
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
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.
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)
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.
Exclusivity structures and graph representatives of local complementation orbits
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.
Temporal Representation in Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
International Nuclear Information System (INIS)
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
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.
Building Scalable Knowledge Graphs for Earth Science
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.
A generalization of total graphs
Indian Academy of Sciences (India)
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
Indian Academy of Sciences (India)
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Wielicki, B. A. (Principal Investigator); Barkstrom, B. R. (Principal Investigator); Charlock, T. P.; Baum, B. A.; Green, R. N.; Minnis, P.; Smith, G. L.; Coakley, J. A.; Randall, D. R.; Lee, R. B., III
1995-01-01
The theoretical bases for the Release 1 algorithms that will be used to process satellite data for investigation of the Clouds and Earth's Radiant Energy System (CERES) are described. The architecture for software implementation of the methodologies is outlined. Volume 2 details the techniques used to geolocate and calibrate the CERES scanning radiometer measurements of shortwave and longwave radiance to invert the radiances to top-of-the-atmosphere (TOA) and surface fluxes following the Earth Radiation Budget Experiment (ERBE) approach, and to average the fluxes over various time and spatial scales to produce an ERBE-like product. Spacecraft ephemeris and sensor telemetry are used with calibration coefficients to produce a chronologically ordered data product called bidirectional scan (BDS) radiances. A spatially organized instrument Earth scan product is developed for the cloud-processing subsystem. The ERBE-like inversion subsystem converts BDS radiances to unfiltered instantaneous TOA and surface fluxes. The TOA fluxes are determined by using established ERBE techniques. Hourly TOA fluxes are computed from the instantaneous values by using ERBE methods. Hourly surface fluxes are estimated from TOA fluxes by using simple parameterizations based on recent research. The averaging process produces daily, monthly-hourly, and monthly means of TOA and surface fluxes at various scales. This product provides a continuation of the ERBE record.
Mizan: Optimizing Graph Mining in Large Parallel Systems
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.
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.
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.)
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)
Spectral fluctuations of quantum graphs
International Nuclear Information System (INIS)
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry