Completely Described Undirected Graph Structure
Directory of Open Access Journals (Sweden)
G. S. Ivanova
2016-01-01
Full Text Available The objects of research are undirected graphs. The paper considers a problem of their isomorphism. A literature analysis of its solution, has shown that there is no way to define a complete graph invariant in the form of unique structural characteristics of each its vertex, which has a computational complexity of definition better than О (n 4 .The work objective is to provide the characteristics of the graph structure, which could be used to solve the problem of their isomorphism for a time better than О (n 4 . As such characteristics, the paper proposes to use the set of codes of tree roots of all the shortest - in terms of the number of edges - paths from each vertex to the others, uniquely defining the structure of each tree. It proves the theorem that it is possible to reduce the problem of isomorphism of the undirected graphs to the isomorphism problem of their splitting into the trees of all the shortest - in terms of the number of edges - paths of each vertex to the others. An algorithm to construct the shortest paths from each vertex to all others and to compute codes of their vertices has been developed. As the latter, are used Aho-codes, which find application in recognising the isomorphism of trees. The computational complexity to obtain structural characteristics of vertices has been estimated to be about О (n 3 .The pilot studies involved the full-scale experiment using the developed complex programmes to generate raw data, i.e. analytic representation of the graph with the number of vertices equal to 1200, and a programme to provide codes of the tree roots. To have an estimate of - "the worst" in terms of time - complexity of expansion algorithm of graphs into trees of the shortest paths and define the codes of their roots has been an experimentally studied how the number of tree vertices depends on the graph density. For the worst case was obtained a dependence of the number of tree vertices on the number of graph vertices
A Note on the PageRank of Undirected Graphs
Grolmusz, Vince
2012-01-01
The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the literature it is widely noted that the PageRank for undirected graphs are proportional to the degrees of the vertices of the graph. We prove that statement for a particular personalization vector in the definition of the PageRank, and we also show that in gene...
Bounds for percolation thresholds on directed and undirected graphs
Hamilton, Kathleen; Pryadko, Leonid
2015-03-01
Percolation theory is an efficient approach to problems with strong disorder, e.g., in quantum or classical transport, composite materials, and diluted magnets. Recently, the growing role of big data in scientific and industrial applications has led to a renewed interest in graph theory as a tool for describing complex connections in various kinds of networks: social, biological, technological, etc. In particular, percolation on graphs has been used to describe internet stability, spread of contagious diseases and computer viruses; related models describe market crashes and viral spread in social networks. We consider site-dependent percolation on directed and undirected graphs, and present several exact bounds for location of the percolation transition in terms of the eigenvalues of matrices associated with graphs, including the adjacency matrix and the Hashimoto matrix used to enumerate non-backtracking walks. These bounds correspond t0 a mean field approximation and become asymptotically exact for graphs with no short cycles. We illustrate this convergence numerically by simulating percolation on several families of graphs with different cycle lengths. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.
Buscema, Massimo; Asadi-Zeydabadi, Masoud; Lodwick, Weldon; Breda, Marco
2016-04-01
Significant applications such as the analysis of Alzheimer's disease differentiated from dementia, or in data mining of social media, or in extracting information of drug cartel structural composition, are often modeled as graphs. The structural or topological complexity or lack of it in a graph is quite often useful in understanding and more importantly, resolving the problem. We are proposing a new index we call the H0function to measure the structural/topological complexity of a graph. To do this, we introduce the concept of graph pruning and its associated algorithm that is used in the development of our measure. We illustrate the behavior of our measure, the H0 function, through different examples found in the appendix. These examples indicate that the H0 function contains information that is useful and important characteristics of a graph. Here, we restrict ourselves to undirected.
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...
Hindersin, Laura; Traulsen, Arne
2015-01-01
We analyze evolutionary dynamics on graphs, where the nodes represent individuals of a population. The links of a node describe which other individuals can be displaced by the offspring of the individual on that node. Amplifiers of selection are graphs for which the fixation probability is increased for advantageous mutants and decreased for disadvantageous mutants. A few examples of such amplifiers have been developed, but so far it is unclear how many such structures exist and how to construct them. Here, we show that almost any undirected random graph is an amplifier of selection for Birth-death updating, where an individual is selected to reproduce with probability proportional to its fitness and one of its neighbors is replaced by that offspring at random. If we instead focus on death-Birth updating, in which a random individual is removed and its neighbors compete for the empty spot, then the same ensemble of graphs consists of almost only suppressors of selection for which the fixation probability is decreased for advantageous mutants and increased for disadvantageous mutants. Thus, the impact of population structure on evolutionary dynamics is a subtle issue that will depend on seemingly minor details of the underlying evolutionary process. PMID:26544962
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.
1990-06-01
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Hard graphs for the maximum clique problem
Hoede, C.
1988-01-01
The maximum clique problem is one of the NP-complete problems. There are graphs for which a reduction technique exists that transforms the problem for these graphs into one for graphs with specific properties in polynomial time. The resulting graphs do not grow exponentially in order and number.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 12; Issue 1. A Problem in Graph Theory. K P Savithri. Think It Over Volume 12 Issue 1 January 2007 pp 81-81. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/012/01/0081-0081. Author Affiliations.
The optimal graph partitioning problem
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Holm, Søren
1993-01-01
In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal. This pr......In this paper we consider the problem of partitioning the set of nodes in a graph in at most p classes, such that the sum of node weights in any class is not greater than the class capacity b, and such that the sum of edge weights, for edges connecting nodes in the same class, is maximal...
DEFF Research Database (Denmark)
Brodal, G.S.; Fagerberg, Rolf; Meyer, U.
2004-01-01
We present improved cache-oblivious data structures and algorithms for breadth-first search and the single-source shortest path problem on undirected graphs with non-negative edge weights. Our results removes the performance gap between the currently best cache-aware algorithms for these problems...
Chinese Postman Problem on edge-colored multigraphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
It is well-known that the Chinese Postman Problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese Postman Problem on mixed graphs, i.e., graphs with directed and undirected edges......, for which the problem is NP-hard....
Constrained Graph Optimization: Interdiction and Preservation Problems
Energy Technology Data Exchange (ETDEWEB)
Schild, Aaron V [Los Alamos National Laboratory
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
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.)
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.)
The direct algorithm for solving of the graph isomorphism problem
Faizullin, Rashit T.; Prolubnikov, Alexander V.
2005-01-01
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
On the Existence of t-Identifying Codes in Undirected De Bruijn Networks
2015-08-04
UNDIRECTED DE BRUIJN NETWORKS 5a. CONTRACT NUMBER NA 5b. GRANT NUMBER NA 5c. PROGRAM ELEMENT NUMBER 62788F 6. AUTHOR(S) Victoria Horan 5d. PROJECT...remaining cases remain open. Additionally, we show that the eccentricity of the undirected non-binary de Bruijn graph is n. 15. SUBJECT TERMS...Additionally, we show that the eccentricity of the undirected non-binary de Bruijn graph is n. 1 Introduction and Background Let x ∈ V (G), and
Amplification on Undirected Population Structures: Comets Beat Stars.
Pavlogiannis, Andreas; Tkadlec, Josef; Chatterjee, Krishnendu; Nowak, Martin A
2017-03-06
The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure. Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade. In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
Solving graph problems with dynamic computation structures
Babb, Jonathan W.; Frank, Matthew; Agarwal, Anant
1996-10-01
We introduce dynamic computation structures (DCS), a compilation technique to produce dynamic code for reconfigurable computing. DCS specializes directed graph instances into user-level hardware for reconfigurable architectures. Several problems such as shortest path and transitive closure exhibit the general properties of closed semirings, an algebraic structure for solving directed paths. Motivating our application domain choice of closed semiring problems is the fact that logic emulation software already maps a special case of directed graphs, namely logic netlists, onto arrays of field programmable gate arrays (FPGA). A certain type of logic emulation software called virtual wires further allows an FPGA array to be viewed as a machine-independent computing fabric. Thus, a virtual wires compiler, coupled with front-end commercial behavioral logic synthesis software, enables automatic behavioral compilation into a multi-FPGA computing fabric. We have implemented a DCS front-end compiler to parallelize the entire inner loop of the classic Bellman-Ford algorithm into synthesizable behavioral verilog. Leveraging virtual wire compilation and behavioral synthesis, we have automatically generated designs of 14 to 261 FPGAs from a single graph instance. We achieve speedups proportional to the number of graph edges - - from 10X to almost 400X versus a 125 SPECint SparcStation 10.
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.
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
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Directory of Open Access Journals (Sweden)
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
A bicriterion Steiner tree problem on graph
Directory of Open Access Journals (Sweden)
Vujošević Mirko B.
2003-01-01
Full Text Available This paper presents a formulation of bicriterion Steiner tree problem which is stated as a task of finding a Steiner tree with maximal capacity and minimal length. It is considered as a lexicographic multicriteria problem. This means that the bottleneck Steiner tree problem is solved first. After that, the next optimization problem is stated as a classical minimums Steiner tree problem under the constraint on capacity of the tree. The paper also presents some computational experiments with the multicriteria problem.
Modified Classical Graph Algorithms for the DNA Fragment Assembly Problem
Directory of Open Access Journals (Sweden)
Guillermo M. Mallén-Fullerton
2015-09-01
Full Text Available DNA fragment assembly represents an important challenge to the development of efficient and practical algorithms due to the large number of elements to be assembled. In this study, we present some graph theoretical linear time algorithms to solve the problem. To achieve linear time complexity, a heap with constant time operations was developed, for the special case where the edge weights are integers and do not depend on the problem size. The experiments presented show that modified classical graph theoretical algorithms can solve the DNA fragment assembly problem efficiently.
Analyzing Traffic Problem Model With Graph Theory Algorithms
Tan, Yong
2014-01-01
This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with combinatorial method and graph theory algorithms; how to optimize our strategy to gain a feasible solution through employing other principles of Computer Science.
The traveling salesman problem on cubic and subcubic graphs
S. Boyd; R.A. Sitters (René); S.L. van der Ster; L. Stougie (Leen)
2014-01-01
htmlabstractWe study the traveling salesman problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3-conjecture for metric TSP, which says that the integrality gap, i.e., the worst case
The Power of Data Reduction : Kernels for Fundamental Graph Problems
Jansen, B.M.P.
2013-01-01
The purpose of this thesis is to give a mathematical analysis of the power of data reduction for dealing with fundamental NP-hard graph problems. It has often been observed that the use of heuristic reduction rules in a preprocessing phase gives significant performance gains when solving such
Experimental quantum annealing: case study involving the graph isomorphism problem
Zick, Kenneth M.; Shehab, Omar; French, Matthew
2015-01-01
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973
A DNA Computing Model for the Graph Vertex Coloring Problem Based on a Probe Graph
Directory of Open Access Journals (Sweden)
Jin Xu
2018-02-01
Full Text Available The biggest bottleneck in DNA computing is exponential explosion, in which the DNA molecules used as data in information processing grow exponentially with an increase of problem size. To overcome this bottleneck and improve the processing speed, we propose a DNA computing model to solve the graph vertex coloring problem. The main points of the model are as follows: ① The exponential explosion problem is solved by dividing subgraphs, reducing the vertex colors without losing the solutions, and ordering the vertices in subgraphs; and ② the bio-operation times are reduced considerably by a designed parallel polymerase chain reaction (PCR technology that dramatically improves the processing speed. In this article, a 3-colorable graph with 61 vertices is used to illustrate the capability of the DNA computing model. The experiment showed that not only are all the solutions of the graph found, but also more than 99% of false solutions are deleted when the initial solution space is constructed. The powerful computational capability of the model was based on specific reactions among the large number of nanoscale oligonucleotide strands. All these tiny strands are operated by DNA self-assembly and parallel PCR. After thousands of accurate PCR operations, the solutions were found by recognizing, splicing, and assembling. We also prove that the searching capability of this model is up to O(359. By means of an exhaustive search, it would take more than 896 000 years for an electronic computer (5 × 1014 s−1 to achieve this enormous task. This searching capability is the largest among both the electronic and non-electronic computers that have been developed since the DNA computing model was proposed by Adleman’s research group in 2002 (with a searching capability of O(220. Keywords: DNA computing, Graph vertex coloring problem, Polymerase chain reaction
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 uses several classes of facet-defining inequalities as cuttingplanes. These are b-tree, clique, cycle with ear, multistar, and S, Tinequalities. Descriptions of the separation procedures that are used for these inequality classes are also given. In order to evaluate the usefulness of the inequalities...... and the overall performance of the branch-and-cut algorithm several computational experiments are conducted. We present some of the results of these experiments....
Dirichlet-Neumann bracketing for boundary-value problems on graphs
Directory of Open Access Journals (Sweden)
Sonja Currie
2005-08-01
Full Text Available We consider the spectral structure of second order boundary-value problems on graphs. A variational formulation for boundary-value problems on graphs is given. As a consequence we can formulate an analogue of Dirichlet-Neumann bracketing for boundary-value problems on graphs. This in turn gives rise to eigenvalue and eigenfunction asymptotic approximations.
Categorical constructions in graph theory
Directory of Open Access Journals (Sweden)
Richard T. Bumby
1986-01-01
Full Text Available This paper presents some graph-theoretic questions from the viewpoint of the portion of category theory which has become common knowledge. In particular, the reader is encouraged to consider whether there is only one natural category of graphs and how theories of directed graphs and undirected graphs are related.
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
Kar, Tugrul
2016-01-01
This study examined prospective middle school mathematics teachers' problem-posing skills by investigating their ability to associate linear graphs with daily life situations. Prospective teachers were given linear graphs and asked to pose problems that could potentially be represented by the graphs. Their answers were analyzed in two stages. In…
Graph theory favorite conjectures and open problems 1
Hedetniemi, Stephen; Larson, Craig
2016-01-01
This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors’ favorite conjectures and open problems, enhancing the reader’s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled “My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In...
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
DEFF Research Database (Denmark)
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently...... conjectured by Baudon et al. that every undirected graph admits a decomposition into at most three locally irregular graphs, except for a well-characterized set of indecomposable graphs. We herein consider an oriented version of this conjecture. Namely, can every oriented graph be decomposed into at most...... three locally irregular oriented graphs, i.e. whose adjacent vertices have distinct outdegrees? We start by supporting this conjecture by verifying it for several classes of oriented graphs. We then prove a weaker version of this conjecture. Namely, we prove that every oriented graph can be decomposed...
Liu, Chunmei; Song, Yinglei
2010-04-15
In this paper, we study the parameterized complexity of Dominating Set problem in chordal graphs and near chordal graphs. We show the problem is W[2]-hard and cannot be solved in time n o(k) in chordal and s -chordal ( s > 3) graphs unless W[1]=FPT. In addition, we obtain inapproximability results for computing a minimum dominating set in chordal and near chordal graphs. Our results prove that unless NP=P, the minimum dominating set in a chordal or s -chordal ( s > 3) graph cannot be approximated within a ratio of [Formula: see text] ln n in polynomial time, where n is the number of vertices in the graph and 0 graphs. In other words, our results suggest that restricting to chordal or s -chordal graphs can improve the approximation ratio by no more than a factor of 3. We then extend our techniques to find similar results for the Independent Dominating Set problem and the Connected Dominating Set problem in chordal or near chordal graphs.
On a directed tree problem motivated by a newly introduced graph product
Directory of Open Access Journals (Sweden)
Antoon H. Boode
2015-10-01
Full Text Available In this paper we introduce and study a directed tree problem motivated by a new graph product that we have recently introduced and analysed in two conference contributions in the context of periodic real-time processes. While the two conference papers were focussing more on the applications, here we mainly deal with the graph theoretical and computational complexity issues. We show that the directed tree problem is NP-complete and present and compare several heuristics for this problem.
RANGI: a fast list-colored graph motif finding algorithm.
Rudi, Ali Gholami; Shahrivari, Saeed; Jalili, Saeed; Moghadam Kashani, Zahra Razaghi
2013-01-01
Given a multiset of colors as the query and a list-colored graph, i.e., an undirected graph with a set of colors assigned to each of its vertices, in the NP-hard list-colored graph motif problem the goal is to find the largest connected subgraph such that one can select a color from the set of colors assigned to each of its vertices to obtain a subset of the query. This problem was introduced to find functional motifs in biological networks. We present a branch-and-bound algorithm named RANGI for finding and enumerating list-colored graph motifs. As our experimental results show, RANGI's pruning methods and heuristics make it quite fast in practice compared to the algorithms presented in the literature. We also present a parallel version of RANGI that achieves acceptable scalability.
PROBLEMS IN TOPOLOGICAL GRAPH THEORY : QUESTIONS I CAN'T ANSWER
Archdeacon, Dan
1999-01-01
This paper describes my Problems in Topological Graph Theory, which can be accessed through the world-wide-web at http: //www.emba .uvm.edu/~arcceack/problems/problems.html This list of problems is constantly being revised; the interested reader is encouraged to submit additions and updates.
On convex relaxation of graph isomorphism
Aflalo, Yonathan; Bronstein, Alexander; Kimmel, Ron
2015-01-01
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic. PMID:25713342
Two-particle quantum walks applied to the graph isomorphism problem
International Nuclear Information System (INIS)
Gamble, John King; Friesen, Mark; Zhou Dong; Joynt, Robert; Coppersmith, S. N.
2010-01-01
We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in which one wishes to determine whether two graphs are isomorphic (related to each other by a relabeling of the graph vertices), and focus on a class of graphs with particularly high symmetry called strongly regular graphs (SRGs). We study the Green's functions that characterize the dynamical evolution single-particle and two-particle quantum walks on pairs of nonisomorphic SRGs and show that interacting particles can distinguish nonisomorphic graphs that noninteracting particles cannot. We obtain the following specific results. (1) We prove that quantum walks of two noninteracting particles, fermions or bosons, cannot distinguish certain pairs of nonisomorphic SRGs. (2) We demonstrate numerically that two interacting bosons are more powerful than single particles and two noninteracting particles, in that quantum walks of interacting bosons distinguish all nonisomorphic pairs of SRGs that we examined. By utilizing high-throughput computing to perform over 500 million direct comparisons between evolution operators, we checked all tabulated pairs of nonisomorphic SRGs, including graphs with up to 64 vertices. (3) By performing a short-time expansion of the evolution operator, we derive distinguishing operators that provide analytic insight into the power of the interacting two-particle quantum walk.
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 and M is the size of internal memory. For weighted undirected graphs we present a cache-aware APSP algorithm that performs O(V · ( V E B +E B log E B )) I/Os. We also present efficient cacheaware algorithms that find paths between all pairs of vertices in an unweighted graph with lengths within a small...... additive constant of the shortest path length. All of our results improve earlier results known for these problems. For approximate APSP we provide the first nontrivial results. Our diameter result uses O(V + E) extra space, and all of our other algorithms use O(V 2) space....
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
DEFF Research Database (Denmark)
Cai, Leizhen; Cheng, Yongxi; Verbin, Elad
2010-01-01
The firefighter problem is the following discrete-time game on a graph. Initially, a fire starts at a vertex of the graph. In each round, a firefighter protects one vertex not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefig...... of Cai and Wang [SIAM J. Discrete Math., 23 (2009), pp. 1814-1826] in affirmative....
Computing the Dilation of Edge-Augmented Graphs Embedded in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2008-01-01
Let G = (V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how...... to improve running time to O(n^3*log n) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G U {(u,v)} for every pair of distinct vertices u and v....
Computing the dilation of edge-augmented graphs in metric spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2010-01-01
Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how...... to improve the running time to O(n3logn) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G{(u,v)} for every pair of distinct vertices u and v....
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.
Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
Bradlyn, Barry; Elcoro, L.; Vergniory, M. G.; Cano, Jennifer; Wang, Zhijun; Felser, C.; Aroyo, M. I.; Bernevig, B. Andrei
2018-01-01
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature (London) 547, 298 (2017), 10.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k .p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.
Solving the replacement paths problem for planar directed graphs in O(n logn) time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2010-01-01
In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace...
Exponential-Time Algorithms and Complexity of NP-Hard Graph Problems
DEFF Research Database (Denmark)
Taslaman, Nina Sofia
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 of...
Knowledge graph analysis of some particular problems in the semantics of Chinese
Hoede, C.; Li, Xueliang; Li, X.; Liu, X; Zhang, Lei
2000-01-01
Knowledge graph theory aims at giving an analysis of language in general. The theory is tested on some particular problems in the semantics of Chinese. These problems concern word formation and the use of verbs. It is attempted to understand how words are formed and how the verb is used in Chinese
Directory of Open Access Journals (Sweden)
Lely Hiryanto
2012-05-01
Full Text Available University Course Timetabling Problem merupakan proses penjadwalan mata kuliah di sebuah universitas yang hasilnya diusahakan seoptimal mungkin untuk tidak saling berbenturan dengan batasan-batasan dan syarat-syarat (constraints tertentu. Dalam menentukan penjadwalan berbasis perhitungan, salah satu metode yang dapat digunakan adalah Graph Coloring. Graph Coloring merupakan merupakan metode yang paling sederhana dan dapat digunakan untuk menentukan penjadwalan yang memiliki berbagai macam constraints. Pada penelitian ini, peneliti mengusulkan pengembangan dari metode Graph Coloring yang ada untuk membuat penjadwalan mata kuliah yang optimal dengan memertimbangkan berbagai macam constraints. Pengembangan ini diujicobakan ke penjadwalan mata kuliah di Fakultas Teknologi Informasi Universitas Tarumanagara (FTI Untar. Hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Rata-rata 7% pelanggaran constraints dikarenakan keterbatasan jumlah ruang dan total slot waktu kuliah, serta permintaan jadwal tertentu oleh dosen. University Course timetabling problem is the process of scheduling courses at a university whose results are optimally arranged to not collide with the limits and conditions (constraints specified. In determining the scheduling komputatif, one method that can be used is the Graph Coloring. Graph Coloring is the simplest method and can be used to determine which have a variety of scheduling constraints. In the present study, the researcher proposes the development of the existing methods of Graph Coloring to make optimal scheduling of courses taking into account various constraints. This development was tested to the scheduling of courses in the Faculty of Information Technology University Tarumanagara (FTI Untar. The experimental results show that the development of methods of Graph Coloring deliver results that meet the
GRAMI: Generalized Frequent Subgraph Mining in Large Graphs
El Saeedy, Mohammed El Sayed
2011-07-24
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper we propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. We developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. We also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. Our experiments on real data demonstrate that our framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
Solving the Replacement Paths Problem for Planar Directed Graphs in O(nlog n) Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P, the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linear-space...... algorithm with O(nlog n) running time for n-vertex planar directed graphs. The previous best time bound was O(n(log n)^2)....
Solving Problem of Graph Isomorphism by Membrane-Quantum Hybrid Model
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Artiom Alhazov
2015-10-01
Full Text Available This work presents the application of new parallelization methods based on membrane-quantum hybrid computing to graph isomorphism problem solving. Applied membrane-quantum hybrid computational model was developed by authors. Massive parallelism of unconventional computing is used to implement classic brute force algorithm efficiently. This approach does not suppose any restrictions of considered graphs types. The estimated performance of the model is less then quadratic that makes a very good result for the problem of \\textbf{NP} complexity.
Gysel, Rob; Gusfield, Dan
2011-01-01
The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.
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.
Scalable Parallel Distributed Coprocessor System for Graph Searching Problems with Massive Data
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Wanrong Huang
2017-01-01
Full Text Available The Internet applications, such as network searching, electronic commerce, and modern medical applications, produce and process massive data. Considerable data parallelism exists in computation processes of data-intensive applications. A traversal algorithm, breadth-first search (BFS, is fundamental in many graph processing applications and metrics when a graph grows in scale. A variety of scientific programming methods have been proposed for accelerating and parallelizing BFS because of the poor temporal and spatial locality caused by inherent irregular memory access patterns. However, new parallel hardware could provide better improvement for scientific methods. To address small-world graph problems, we propose a scalable and novel field-programmable gate array-based heterogeneous multicore system for scientific programming. The core is multithread for streaming processing. And the communication network InfiniBand is adopted for scalability. We design a binary search algorithm to address mapping to unify all processor addresses. Within the limits permitted by the Graph500 test bench after 1D parallel hybrid BFS algorithm testing, our 8-core and 8-thread-per-core system achieved superior performance and efficiency compared with the prior work under the same degree of parallelism. Our system is efficient not as a special acceleration unit but as a processor platform that deals with graph searching applications.
RRES: A Novel Approach to the Partitioning Problem for a Typical Subset of System Graphs
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B. Knerr
2008-03-01
Full Text Available The research field of system partitioning in modern electronic system design started to find strong advertence of scientists about fifteen years ago. Since a multitude of formulations for the partitioning problem exist, the same multitude could be found in the number of strategies that address this problem. Their feasibility is highly dependent on the platform abstraction and the degree of realism that it features. This work originated from the intention to identify the most mature and powerful approaches for system partitioning in order to integrate them into a consistent design framework for wireless embedded systems. Within this publication, a thorough characterisation of graph properties typical for task graphs in the field of wireless embedded system design has been undertaken and has led to the development of an entirely new approach for the system partitioning problem. The restricted range exhaustive search algorithm is introduced and compared to popular and well-reputed heuristic techniques based on tabu search, genetic algorithm, and the global criticality/local phase algorithm. It proves superior performance for a set of system graphs featuring specific properties found in human-made task graphs, since it exploits their typical characteristics such as locality, sparsity, and their degree of parallelism.
RRES: A Novel Approach to the Partitioning Problem for a Typical Subset of System Graphs
Directory of Open Access Journals (Sweden)
Knerr B
2008-01-01
Full Text Available Abstract The research field of system partitioning in modern electronic system design started to find strong advertence of scientists about fifteen years ago. Since a multitude of formulations for the partitioning problem exist, the same multitude could be found in the number of strategies that address this problem. Their feasibility is highly dependent on the platform abstraction and the degree of realism that it features. This work originated from the intention to identify the most mature and powerful approaches for system partitioning in order to integrate them into a consistent design framework for wireless embedded systems. Within this publication, a thorough characterisation of graph properties typical for task graphs in the field of wireless embedded system design has been undertaken and has led to the development of an entirely new approach for the system partitioning problem. The restricted range exhaustive search algorithm is introduced and compared to popular and well-reputed heuristic techniques based on tabu search, genetic algorithm, and the global criticality/local phase algorithm. It proves superior performance for a set of system graphs featuring specific properties found in human-made task graphs, since it exploits their typical characteristics such as locality, sparsity, and their degree of parallelism.
Spin glass phase transitions in the random feedback vertex set problem
Qin, Shao-Meng; Zeng, Ying; Zhou, Hai-Jun
2016-01-01
A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be efficiently solved after converting it into an appropriate spin glass model [H.-J. Zhou, Eur. Phys. J. B 86 (2013) 455]. In the present work we study the local stability and the phase transition properties of this spin glass model on random graphs. For both regul...
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.
The development of e-learning applications solving problems from graph theory
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Pavel Kolman
2013-01-01
Full Text Available Authors are in long term developing e-learning supports for some parts of Operation Research course. The original purpose was to prepare e-learning supports for students of FBE Mendelu, mainly for part-time form students, who have subscribed Economic mathematical methods course (EMM. Considering decreasing number of lessons on part-time form of study (16 hours in a semester, in comparison to 56 hours in full-time form of study, was for part-time form students even more difficult to fulfill exam requirements. As a help for students there was stage by stage prepared several of programs, they allow self-contained practicing of some linear programming methods. Programs did allow to users step-by-step verify their solution, i.e. whether their calculation are in accordance with algorithm described in lectures. Advantage for the students consists in fact, that each mistake (numerical or algorithmic they were able to uncover, what contributes to increase of self-study effectiveness and from that resulting higher study motivation. Resulting from existing experience, authors decided to request for a new FRVŠ grant for academic year 2012, focused on e-learning support of selected graph theory problems. Within this project there was developed a tool allowing to make and according to the user needs interactively modify created graphs. On this graph it is possible individually, step by step (in compliance with on lectures presented algorithm to practice solving of selected graph theory and network analysis problems (e.g. minimal spanning tree, shortest path in a graph, testing for cycles in a graph, critical path method etc.. Project is realized as modular and was realized in Delphi developing tool. Described algorithms are saved in dynamic linked libraries. There for it is very easy to add here new (newly programmed algorithms. Project results (i.e. project experience obtained from e-learning supports will be available for all FBE Mendelu members interested
The Edge-Disjoint Path Problem on Random Graphs by Message-Passing.
Altarelli, Fabrizio; Braunstein, Alfredo; Dall'Asta, Luca; De Bacco, Caterina; Franz, Silvio
2015-01-01
We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star graph onto a weighted maximum matching problem. We perform extensive numerical simulations on random graphs of various types to test the performance both in terms of path length minimization and maximization of the number of accommodated paths. In addition, we test the performance on benchmark instances on various graphs by comparison with state-of-the-art algorithms and results found in the literature. Our message-passing algorithm always outperforms the others in terms of the number of accommodated paths when considering non trivial instances (otherwise it gives the same trivial results). Remarkably, the largest improvement in performance with respect to the other methods employed is found in the case of benchmarks with meshes, where the validity hypothesis behind message-passing is expected to worsen. In these cases, even though the exact message-passing equations do not converge, by introducing a reinforcement parameter to force convergence towards a sub optimal solution, we were able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths. On random graphs, we numerically observe two separated regimes: one in which all paths can be accommodated and one in which this is not possible. We also investigate the behavior of both the number of paths to be accommodated and their minimum total length.
Families of Fixed Degree Graphs for Processor Interconnection
DEFF Research Database (Denmark)
Jerrum, Mark; Skyum, Sven
1984-01-01
A construction is presented which, given a fixed undirected graph of low degree and small average path length, yields an infinite sequence of low diameter graphs of increasing order and fixed degree. As examples of the construction, infinite sequences of low diameter graphs are presented with deg...
Wahid, Juliana; Hussin, Naimah Mohd
2016-08-01
The construction of population of initial solution is a crucial task in population-based metaheuristic approach for solving curriculum-based university course timetabling problem because it can affect the convergence speed and also the quality of the final solution. This paper presents an exploration on combination of graph heuristics in construction approach in curriculum based course timetabling problem to produce a population of initial solutions. The graph heuristics were set as single and combination of two heuristics. In addition, several ways of assigning courses into room and timeslot are implemented. All settings of heuristics are then tested on the same curriculum based course timetabling problem instances and are compared with each other in terms of number of population produced. The result shows that combination of saturation degree followed by largest degree heuristic produce the highest number of population of initial solutions. The results from this study can be used in the improvement phase of algorithm that uses population of initial solutions.
Contributions to combinatorics on words in an abelian context and covering problems in graphs
Vandomme, Elise
2015-01-01
This thesis dissertation is divided into two (distinct but connected) parts that reflect the joint PhD. We study and we solve several questions regarding on the one hand combinatorics on words in an abelian context and on the other hand covering problems in graphs. Each particular problem is the topic of a chapter. In combinatorics on words, the first problem considered focuses on the 2-regularity of sequences in the sense of Allouche and Shallit. We prove that a sequence satisfying a ce...
Directory of Open Access Journals (Sweden)
Jean Chamberlain Chedjou
2015-01-01
Full Text Available This paper develops a flexible analytical concept for robust shortest path detection in dynamically reconfigurable graphs. The concept is expressed by a mathematical model representing the shortest path problem solver. The proposed mathematical model is characterized by three fundamental parameters expressing (a the graph topology (through the “incidence matrix”, (b the edge weights (with dynamic external weights’ setting capability, and (c the dynamic reconfigurability through external input(s of the source-destination nodes pair. In order to demonstrate the universality of the developed concept, a general algorithm is proposed to determine the three fundamental parameters (of the mathematical model developed for all types of graphs regardless of their topology, magnitude, and size. It is demonstrated that the main advantage of the developed concept is that arc costs, the origin-destination pair setting, and the graph topology are dynamically provided by external commands, which are inputs of the shortest path solver model. This enables high flexibility and full reconfigurability of the developed concept, without any retraining need. To validate the concept developed, benchmarking is performed leading to a comparison of its performance with the performances of two well-known concepts based on neural networks.
Chemical Graph Transformation with Stereo-Information
DEFF Research Database (Denmark)
Andersen, Jakob Lykke; Flamm, Christoph; Merkle, Daniel
2017-01-01
Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms and their neighbo......Double Pushout graph transformation naturally facilitates the modelling of chemical reactions: labelled undirected graphs model molecules and direct derivations model chemical reactions. However, the most straightforward modelling approach ignores the relative placement of atoms...... and their neighbours in space. Stereoisomers of chemical compounds thus cannot be distinguished, even though their chemical activity may differ substantially. In this contribution we propose an extended chemical graph transformation system with attributes that encode information about local geometry. The modelling...... of graph transformation, but we here propose a framework that also allows for partially specified stereoinformation. While there are several stereochemical configurations to be considered, we focus here on the tetrahedral molecular shape, and suggest general principles for how to treat all other chemically...
DEFF Research Database (Denmark)
Hartnell, B.L.; Vestergaard, Preben Dahl
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 graph that remains can still be decomposed (such graphs are called or ). In this paper we consider the follwing variation. Given a fixed graph H, determine which graphs (call them ) have the property that every edge disjoint packing with H is maximum. In the case that the graph H is isomorphic...... to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more. randomly packable randomly decomposable equipackable maximal...
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 graph that remains can still be decomposed (such graphs are called randomly packable or randomly decomposable). In this paper we consider the following variation. Given a fixed graph H, determine which graphs (call them equipackable) have the property that every maximal edge disjoint packing with H...... is maximum. In the case that the graph H is isomorphic to the path on 3 nodes, we characterize the equipackable graphs of girth 5 or more....
Detecting Statistically Significant Communities of Triangle Motifs in Undirected Networks
2016-04-26
extend the work of Perry et al. [6] by developing a statistical framework that supports the detection of triangle motif- based clusters in complex...priori, the need for triangle motif- based clustering. 2. Developed an algorithm for clustering undirected networks, where the triangle con guration was...13 5 Application to Real Networks 18 5.1 2012 FBS Football Schedule Network
Assessing statistical significance in causal graphs.
Chindelevitch, Leonid; Loh, Po-Ru; Enayetallah, Ahmed; Berger, Bonnie; Ziemek, Daniel
2012-02-20
Causal graphs are an increasingly popular tool for the analysis of biological datasets. In particular, signed causal graphs--directed graphs whose edges additionally have a sign denoting upregulation or downregulation--can be used to model regulatory networks within a cell. Such models allow prediction of downstream effects of regulation of biological entities; conversely, they also enable inference of causative agents behind observed expression changes. However, due to their complex nature, signed causal graph models present special challenges with respect to assessing statistical significance. In this paper we frame and solve two fundamental computational problems that arise in practice when computing appropriate null distributions for hypothesis testing. First, we show how to compute a p-value for agreement between observed and model-predicted classifications of gene transcripts as upregulated, downregulated, or neither. Specifically, how likely are the classifications to agree to the same extent under the null distribution of the observed classification being randomized? This problem, which we call "Ternary Dot Product Distribution" owing to its mathematical form, can be viewed as a generalization of Fisher's exact test to ternary variables. We present two computationally efficient algorithms for computing the Ternary Dot Product Distribution and investigate its combinatorial structure analytically and numerically to establish computational complexity bounds.Second, we develop an algorithm for efficiently performing random sampling of causal graphs. This enables p-value computation under a different, equally important null distribution obtained by randomizing the graph topology but keeping fixed its basic structure: connectedness and the positive and negative in- and out-degrees of each vertex. We provide an algorithm for sampling a graph from this distribution uniformly at random. We also highlight theoretical challenges unique to signed causal graphs
Multi-label Learning with Missing Labels Using Mixed Dependency Graphs
Wu, Baoyuan
2018-04-06
This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels (i.e., some of their labels are missing). The key point to handle missing labels is propagating the label information from the provided labels to missing labels, through a dependency graph that each label of each instance is treated as a node. We build this graph by utilizing different types of label dependencies. Specifically, the instance-level similarity is served as undirected edges to connect the label nodes across different instances and the semantic label hierarchy is used as directed edges to connect different classes. This base graph is referred to as the mixed dependency graph, as it includes both undirected and directed edges. Furthermore, we present another two types of label dependencies to connect the label nodes across different classes. One is the class co-occurrence, which is also encoded as undirected edges. Combining with the above base graph, we obtain a new mixed graph, called mixed graph with co-occurrence (MG-CO). The other is the sparse and low rank decomposition of the whole label matrix, to embed high-order dependencies over all labels. Combining with the base graph, the new mixed graph is called as MG-SL (mixed graph with sparse and low rank decomposition). Based on MG-CO and MG-SL, we further propose two convex transductive formulations of the MLML problem, denoted as MLMG-CO and MLMG-SL respectively. In both formulations, the instance-level similarity is embedded through a quadratic smoothness term, while the semantic label hierarchy is used as a linear constraint. In MLMG-CO, the class co-occurrence is also formulated as a quadratic smoothness term, while the sparse and low rank decomposition is incorporated into MLMG-SL, through two additional matrices (one is assumed as sparse, and the other is assumed as low
Pinsky, Ross G
2014-01-01
The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a mélange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
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.
GraMi: Generalized Frequent Pattern Mining in a Single Large Graph
Saeedy, Mohammed El
2011-11-01
Mining frequent subgraphs is an important operation on graphs. Most existing work assumes a database of many small graphs, but modern applications, such as social networks, citation graphs or protein-protein interaction in bioinformatics, are modeled as a single large graph. Interesting interactions in such applications may be transitive (e.g., friend of a friend). Existing methods, however, search for frequent isomorphic (i.e., exact match) subgraphs and cannot discover many useful patterns. In this paper the authors propose GRAMI, a framework that generalizes frequent subgraph mining in a large single graph. GRAMI discovers frequent patterns. A pattern is a graph where edges are generalized to distance-constrained paths. Depending on the definition of the distance function, many instantiations of the framework are possible. Both directed and undirected graphs, as well as multiple labels per vertex, are supported. The authors developed an efficient implementation of the framework that models the frequency resolution phase as a constraint satisfaction problem, in order to avoid the costly enumeration of all instances of each pattern in the graph. The authors also implemented CGRAMI, a version that supports structural and semantic constraints; and AGRAMI, an approximate version that supports very large graphs. The experiments on real data demonstrate that the authors framework is up to 3 orders of magnitude faster and discovers more interesting patterns than existing approaches.
DEFF Research Database (Denmark)
Merker, Martin
The topic of this PhD thesis is graph decompositions. While there exist various kinds of decompositions, this thesis focuses on three problems concerning edgedecompositions. Given a family of graphs H we ask the following question: When can the edge-set of a graph be partitioned so that each part...... k(T)-edge-connected graph whose size is divisible by the size of T admits a T-decomposition. This proves a conjecture by Barát and Thomassen from 2006. Moreover, we introduce a new arboricity notion where we restrict the diameter of the trees in a decomposition into forests. We conjecture......-connected planar graph contains two edge-disjoint 18/19 -thin spanning trees. Finally, we make progress on a conjecture by Baudon, Bensmail, Przybyło, and Wozniak stating that if a graph can be decomposed into locally irregular graphs, then there exists such a decomposition with at most 3 parts. We show...
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.
Infinite graphs in systematic biology, with an application to the species problem.
Alexander, Samuel A
2013-06-01
We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T. A. Knight and C. Darwin, and sketch a decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels' question, "Can biology lead to new theorems?"
Reducing the generalised Sudoku problem to the Hamiltonian cycle problem
Directory of Open Access Journals (Sweden)
Michael Haythorpe
2016-12-01
Full Text Available The generalised Sudoku problem with N symbols is known to be NP-complete, and hence is equivalent to any other NP-complete problem, even for the standard restricted version where N is a perfect square. In particular, generalised Sudoku is equivalent to the, classical, Hamiltonian cycle problem. A constructive algorithm is given that reduces generalised Sudoku to the Hamiltonian cycle problem, where the resultant instance of Hamiltonian cycle problem is sparse, and has O(N3 vertices. The Hamiltonian cycle problem instance so constructed is a directed graph, and so a (known conversion to undirected Hamiltonian cycle problem is also provided so that it can be submitted to the best heuristics. A simple algorithm for obtaining the valid Sudoku solution from the Hamiltonian cycle is provided. Techniques to reduce the size of the resultant graph are also discussed.
Graphs inducing totally balanced and submodular Chinese postman games
Josune Albizuri, M.; Hamers, H.J.M.
2014-01-01
A Chinese postman (CP) game is induced by a weighted undirected, connected graph in which the edges are identified as players and a vertex is chosen as post-office location. Granot and Granot (2012) characterized graphs that give rise to CP games that are balanced. This note completes this line of
De Bruijn graphs and DNA graphs
Pendavingh, Rudi; Schuurman, Petra; Woeginger, Gerhard; Brandstädt, Andreas; Le, Van Bang
2001-01-01
In this paper we prove the NP-hardness of various recognition problems for subgraphs of De Bruijn graphs. In particular, the recognition of DNA graphs is shown to be NP-hard; DNA graphs are the vertex induced subgraphs of De Bruijn graphs over a four letter alphabet. As a consequence, two open
Graph coloring heuristics for solving examination timetabling problem at Universiti Utara Malaysia
Abdul-Rahman, Syariza; Sobri, Nur Suriani; Omar, Mohd Faizal; Benjamin, Aida Mauziah; Ramli, Razamin
2014-12-01
Examination timetabling is a well-studied combinatorial optimization problem involving scheduling a set of examinations into a restricted number of time-slots while satisfying a defined set of constraints. This paper presents a real-world, capacitated examination timetabling problem from Universiti Utara Malaysia (UUM), Malaysia. This dataset differs from the others reported in the literature with respect to its size, complexity and constraints. Until recently, examination timetabling in UUM is done manually with a little guidance from spreadsheet computer software for checking clashes. The propriety system is unable to do the examination timetabling automatically. Besides, the introduced datasets also consider a new constraint that has never been modeled before in timetabling literature, which is lecturer's preference. Moreover, splitting examination across several rooms and a number of hard constraints such as no mixed duration of examination within individual periods, clashes free schedule and room capacity requirement are also need to be adhered. These constraints provide an additional challenge in solving the examination timetabling problem, mainly at UUM. In this paper, graph coloring heuristics are employed to schedule examinations at each step during timetable construction. We used the concept of bin packing heuristics to assign examination to room with respect to the capacity. Since this is a new dataset and no solutions have been published in the literature yet, we only compare the results with an existing manual solution. It is found that the proposed constructive heuristic able to produce good quality solution for the tested problem. The proposed graph coloring heuristics are proved to be superior to the current method employed by the University and found to perform well in comparison.
A classification of cubic symmetric graphs of order 16p2
Indian Academy of Sciences (India)
In this paper, we classify all connected cubic symmetric graphs of order 16p2 for each prime p. Keywords. Regular coverings; symmetric graphs; invariant subspaces. 1. Introduction. Throughout this paper, graphs are assumed to be finite, simple, undirected and connected. For the group-theoretic concepts and notations not ...
Directory of Open Access Journals (Sweden)
Marco Raberto
Full Text Available In this paper, we outline a model of graph (or network dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.
Graph theory approach to the eigenvalue problem of large space structures
Reddy, A. S. S. R.; Bainum, P. M.
1981-01-01
Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.
Directory of Open Access Journals (Sweden)
Xiaochuan Shi
2017-02-01
Full Text Available New information technology constantly improves the efficiency of social networks. Using optimization and decision models in the context of large data sets attracts extensive attention. This paper investigates a novel mathematical model for designing and optimizing environmental economic policies in a protection zone. The proposed model is referred to as the quadratic knapsack problem with conflict graphs, which is a new variant of the knapsack problem family. Due to the investigated problem processing a high complex structure, in order to solve efficiently the problem, we develop a metaheuristic which is based on the large neighborhood search. The proposed method embeds a construction procedure into a sophistical neighborhood search. For more details, the construction procedure takes charge of finding a starting solution while the investigated neighborhood search is used to generate and explore the solution space issuing from the provided starting solution. In order to highlight our theoretical model, we evaluate the model on a set of complex benchmark data sets. The obtained results demonstrate that the investigated algorithm is competitive and efficient compared to legacy algorithms.
Cavanaugh, Kyle C; Siegel, David A; Raimondi, Peter T; Alberto, Filipe
2014-02-01
The manner in which patches are delineated in spatially realistic metapopulation models will influence the size, connectivity, and extinction and recolonization dynamics of those patches. Most commonly used patch-definition methods focus on identifying discrete, contiguous patches of habitat from a single temporal observation of species occurrence or from a model of habitat suitability. However, these approaches are not suitable for many metapopulation systems where entire patches may not be fully colonized at a given time. For these metapopulation systems, a single large patch of habitat may actually support multiple, interacting subpopulations. The interactions among these subpopulations will be ignored if the patch is treated as a single unit, a situation we term the "mega-patch problem." Mega-patches are characterized by variable intra-patch synchrony, artificially low inter-patch connectivity, and low extinction rates. One way to detect this problem is by using time series data to calculate demographic synchrony within mega-patches. We present a framework for identifying subpopulations in mega-patches using a combination of spatial autocorrelation and graph theory analyses. We apply our approach to southern California giant kelp (Macrocystis pyrifera) forests using a new, long-term (27 years), satellite-based data set of giant kelp canopy biomass. We define metapopulation patches using our method as well as several other commonly used patch delineation methodologies and examine the colonization and extinction dynamics of the metapopulation under each approach. We find that the relationships between patch characteristics such as area and connectivity and the demographic processes of colonizations and extinctions vary among the different patch-definition methods. Our spatial-analysis/graph-theoretic framework produces results that match theoretical expectations better than the other methods. This approach can be used to identify subpopulations in metapopulations
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...
Solution to the SLAM Problem in Low Dynamic Environments Using a Pose Graph and an RGB-D Sensor
Directory of Open Access Journals (Sweden)
Donghwa Lee
2014-07-01
Full Text Available In this study, we propose a solution to the simultaneous localization and mapping (SLAM problem in low dynamic environments by using a pose graph and an RGB-D (red-green-blue depth sensor. The low dynamic environments refer to situations in which the positions of objects change over long intervals. Therefore, in the low dynamic environments, robots have difficulty recognizing the repositioning of objects unlike in highly dynamic environments in which relatively fast-moving objects can be detected using a variety of moving object detection algorithms. The changes in the environments then cause groups of false loop closing when the same moved objects are observed for a while, which means that conventional SLAM algorithms produce incorrect results. To address this problem, we propose a novel SLAM method that handles low dynamic environments. The proposed method uses a pose graph structure and an RGB-D sensor. First, to prune the falsely grouped constraints efficiently, nodes of the graph, that represent robot poses, are grouped according to the grouping rules with noise covariances. Next, false constraints of the pose graph are pruned according to an error metric based on the grouped nodes. The pose graph structure is reoptimized after eliminating the false information, and the corrected localization and mapping results are obtained. The performance of the method was validated in real experiments using a mobile robot system.
Solution to the SLAM problem in low dynamic environments using a pose graph and an RGB-D sensor.
Lee, Donghwa; Myung, Hyun
2014-07-11
In this study, we propose a solution to the simultaneous localization and mapping (SLAM) problem in low dynamic environments by using a pose graph and an RGB-D (red-green-blue depth) sensor. The low dynamic environments refer to situations in which the positions of objects change over long intervals. Therefore, in the low dynamic environments, robots have difficulty recognizing the repositioning of objects unlike in highly dynamic environments in which relatively fast-moving objects can be detected using a variety of moving object detection algorithms. The changes in the environments then cause groups of false loop closing when the same moved objects are observed for a while, which means that conventional SLAM algorithms produce incorrect results. To address this problem, we propose a novel SLAM method that handles low dynamic environments. The proposed method uses a pose graph structure and an RGB-D sensor. First, to prune the falsely grouped constraints efficiently, nodes of the graph, that represent robot poses, are grouped according to the grouping rules with noise covariances. Next, false constraints of the pose graph are pruned according to an error metric based on the grouped nodes. The pose graph structure is reoptimized after eliminating the false information, and the corrected localization and mapping results are obtained. The performance of the method was validated in real experiments using a mobile robot system.
Directory of Open Access Journals (Sweden)
Magnolia Tilca
2014-10-01
Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008
Sotirov, Renata
2017-01-01
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation for the graph bisection problem with a matrix variable of
Min st-cut oracle for planar graphs with near-linear preprocessing time
DEFF Research Database (Denmark)
Borradaile, Glencora; Sankowski, Piotr; Wulff-Nilsen, Christian
2010-01-01
For an undirected n-vertex planar graph G with non-negative edge-weights, we consider the following type of query: given two vertices s and t in G, what is the weight of a min st-cut in G? We show how to answer such queries in constant time with O(n log5 n) preprocessing time and O(n log n) space...... problems in planar graphs, we also obtain an implicit representation of a minimum cycle basis in O(n log5 n) time and O(n log n) space and an explicit representation with additional O(C) time and space where C is the size of the basis. To obtain our results, we require that shortest paths be unique...
Approximate von Neumann entropy for directed graphs.
Ye, Cheng; Wilson, Richard C; Comin, César H; Costa, Luciano da F; Hancock, Edwin R
2014-05-01
In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.
Semisymmetric cubic graphs of order 16p2 16p2 16p2
Indian Academy of Sciences (India)
Abstract. An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order. 16p2. It is shown that for every odd prime p, there exists a ...
Semisymmetric cubic graphs of order 16p2 16p2 16p2
Indian Academy of Sciences (India)
An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order 162. It is shown that for every odd prime , there exists a semisymmetric ...
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.
ML-MG: Multi-label Learning with Missing Labels Using a Mixed Graph
Wu, Baoyuan
2015-12-07
This work focuses on the problem of multi-label learning with missing labels (MLML), which aims to label each test instance with multiple class labels given training instances that have an incomplete/partial set of these labels (i.e. some of their labels are missing). To handle missing labels, we propose a unified model of label dependencies by constructing a mixed graph, which jointly incorporates (i) instance-level similarity and class co-occurrence as undirected edges and (ii) semantic label hierarchy as directed edges. Unlike most MLML methods, We formulate this learning problem transductively as a convex quadratic matrix optimization problem that encourages training label consistency and encodes both types of label dependencies (i.e. undirected and directed edges) using quadratic terms and hard linear constraints. The alternating direction method of multipliers (ADMM) can be used to exactly and efficiently solve this problem. To evaluate our proposed method, we consider two popular applications (image and video annotation), where the label hierarchy can be derived from Wordnet. Experimental results show that our method achieves a significant improvement over state-of-the-art methods in performance and robustness to missing labels.
Directory of Open Access Journals (Sweden)
Vatutin Eduard
2017-12-01
Full Text Available The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
Vatutin, Eduard
2017-12-01
The article deals with the problem of analysis of effectiveness of the heuristic methods with limited depth-first search techniques of decision obtaining in the test problem of getting the shortest path in graph. The article briefly describes the group of methods based on the limit of branches number of the combinatorial search tree and limit of analyzed subtree depth used to solve the problem. The methodology of comparing experimental data for the estimation of the quality of solutions based on the performing of computational experiments with samples of graphs with pseudo-random structure and selected vertices and arcs number using the BOINC platform is considered. It also shows description of obtained experimental results which allow to identify the areas of the preferable usage of selected subset of heuristic methods depending on the size of the problem and power of constraints. It is shown that the considered pair of methods is ineffective in the selected problem and significantly inferior to the quality of solutions that are provided by ant colony optimization method and its modification with combinatorial returns.
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...
HYPERSPECTRAL DATA CLASSIFICATION USING FACTOR GRAPHS
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A. Makarau
2012-07-01
Full Text Available Accurate classification of hyperspectral data is still a competitive task and new classification methods are developed to achieve desired tasks of hyperspectral data use. The objective of this paper is to develop a new method for hyperspectral data classification ensuring the classification model properties like transferability, generalization, probabilistic interpretation, etc. While factor graphs (undirected graphical models are unfortunately not widely employed in remote sensing tasks, these models possess important properties such as representation of complex systems to model estimation/decision making tasks. In this paper we present a new method for hyperspectral data classification using factor graphs. Factor graph (a bipartite graph consisting of variables and factor vertices allows factorization of a more complex function leading to definition of variables (employed to store input data, latent variables (allow to bridge abstract class to data, and factors (defining prior probabilities for spectral features and abstract classes; input data mapping to spectral features mixture and further bridging of the mixture to an abstract class. Latent variables play an important role by defining two-level mapping of the input spectral features to a class. Configuration (learning on training data of the model allows calculating a parameter set for the model to bridge the input data to a class. The classification algorithm is as follows. Spectral bands are separately pre-processed (unsupervised clustering is used to be defined on a finite domain (alphabet leading to a representation of the data on multinomial distribution. The represented hyperspectral data is used as input evidence (evidence vector is selected pixelwise in a configured factor graph and an inference is run resulting in the posterior probability. Variational inference (Mean field allows to obtain plausible results with a low calculation time. Calculating the posterior probability for
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.
Searches over graphs representing geospatial-temporal remote sensing data
Energy Technology Data Exchange (ETDEWEB)
Brost, Randolph; Perkins, David Nikolaus
2018-03-06
Various technologies pertaining to identifying objects of interest in remote sensing images by searching over geospatial-temporal graph representations are described herein. Graphs are constructed by representing objects in remote sensing images as nodes, and connecting nodes with undirected edges representing either distance or adjacency relationships between objects and directed edges representing changes in time. Geospatial-temporal graph searches are made computationally efficient by taking advantage of characteristics of geospatial-temporal data in remote sensing images through the application of various graph search techniques.
Seiller, Thomas
2014-01-01
In two previous papers, we exposed a combinatorial approach to the program of Geometry of Interaction, a program initiated by Jean-Yves Girard. The strength of our approach lies in the fact that we interpret proofs by simpler structures - graphs - than Girard's constructions, while generalizing the latter since they can be recovered as special cases of our setting. This third paper extends this approach by considering a generalization of graphs named graphings, which is in some way a geometri...
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....
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 ...
Asteroidal Quadruples in non Rooted Path Graphs
Directory of Open Access Journals (Sweden)
Gutierrez Marisa
2015-11-01
Full Text Available A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.
A nonlinear merging protocol for consensus in multi-agent systems on signed and weighted graphs
Feng, Shasha; Wang, Li; Li, Yijia; Sun, Shiwen; Xia, Chengyi
2018-01-01
In this paper, we investigate the multi-agent consensus for networks with undirected graphs which are not connected, especially for the signed graph in which some edge weights are positive and some edges have negative weights, and the negative-weight graph whose edge weights are negative. We propose a novel nonlinear merging consensus protocol to drive the states of all agents to converge to the same state zero which is not dependent upon the initial states of agents. If the undirected graph whose edge weights are positive is connected, then the states of all agents converge to the same state more quickly when compared to most other protocols. While the undirected graph whose edge weights might be positive or negative is unconnected, the states of all agents can still converge to the same state zero under the premise that the undirected graph can be divided into several connected subgraphs with more than one node. Furthermore, we also discuss the impact of parameter r presented in our protocol. Current results can further deepen the understanding of consensus processes for multi-agent systems.
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
Chen, Wenbin; Hendrix, William; Samatova, Nagiza F
2017-12-01
The problem of aligning multiple metabolic pathways is one of very challenging problems in computational biology. A metabolic pathway consists of three types of entities: reactions, compounds, and enzymes. Based on similarities between enzymes, Tohsato et al. gave an algorithm for aligning multiple metabolic pathways. However, the algorithm given by Tohsato et al. neglects the similarities among reactions, compounds, enzymes, and pathway topology. How to design algorithms for the alignment problem of multiple metabolic pathways based on the similarity of reactions, compounds, and enzymes? It is a difficult computational problem. In this article, we propose an algorithm for the problem of aligning multiple metabolic pathways based on the similarities among reactions, compounds, enzymes, and pathway topology. First, we compute a weight between each pair of like entities in different input pathways based on the entities' similarity score and topological structure using Ay et al.'s methods. We then construct a weighted k-partite graph for the reactions, compounds, and enzymes. We extract a mapping between these entities by solving the maximum-weighted k-partite matching problem by applying a novel heuristic algorithm. By analyzing the alignment results of multiple pathways in different organisms, we show that the alignments found by our algorithm correctly identify common subnetworks among multiple pathways.
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.
Noble, S D; Welsh, D J A
2000-01-01
We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycle spaces is an effective numerical invariant of these classes.
Total graph of a module with respect to singular submodule
Directory of Open Access Journals (Sweden)
Jituparna Goswami
2016-07-01
Full Text Available Let R be a commutative ring with unity and M be an R-module. We introduce the total graph of a module M with respect to singular submodule Z(M of M as an undirected graph T(Γ(M with vertex set as M and any two distinct vertices x and y are adjacent if and only if x+y∈Z(M. We investigate some properties of the total graph T(Γ(M and its induced subgraphs Z(Γ(M and Z¯(Γ(M. In some aspects, we have noticed some sort of finiteness.
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...
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.
Uncertain Graph Sparsification
Parchas, Panos; Papailiou, Nikolaos; Papadias, Dimitris; Bonchi, Francesco
2016-01-01
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce...
Graph theory and interconnection networks
Hsu, Lih-Hsing
2008-01-01
The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
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.
Minimum Cycle Basis and All-Pairs Min Cut of a Planar Graph in Subquadratic Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2009-01-01
A minimum cycle basis of a weighted undirected graph G is a ba- sis of the cycle space of G such that the total weight of the cycles in this basis is minimized. If G is a planar graph with non-negative edge weights, such a basis can be found in O(n2) time and space, where n is the size of G. We...... equivalent to the minimum cycle basis problem for planar graphs. We also obtain O(n3/2 log n) time and O(n3/2) space algorithms for finding, respectively, the weight vector and a Gomory-Hu tree of G. The previous best time and space bound for these two problems was quadratic. From our Gomory-Hu tree...... show that this is optimal if an explicit represen- tation of the basis is required. We then present an O(n3/2 log n) time and O(n3/2) space algorithm that computes a minimum cycle basis implicitly. From this result, we obtain an output-sensitive algorithm that explicitly computes a minimum cycle basis...
Comparison and Enumeration of Chemical Graphs
Akutsu, Tatsuya; Nagamochi, Hiroshi
2013-01-01
Chemical compounds are usually represented as graph structured data in computers. In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes. In particular, we consider the following problems: determining whether two chemical graphs are identical, determining whether one input chemical graph is a part of the other input chemical graph, finding a maximum common part of two input graphs, finding a reaction atom mapping, enumerating possible chemical graphs, and enumerating stereoisomers. We also discuss the relationship between the fifth problem and kernel functions for chemical compounds. PMID:24688697
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
Consensus problem in directed networks of multi-agents via nonlinear protocols
International Nuclear Information System (INIS)
Liu Xiwei; Chen Tianping; Lu Wenlian
2009-01-01
In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.
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.
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.
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
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.
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
Agreement dynamics on directed random graphs
Lipowski, Adam; Lipowska, Dorota; Ferreira, António Luis
2017-06-01
We examine some agreement-dynamics models that are placed on directed random graphs. In such systems, a fraction of sites \\exp(-z) , where z is the average degree, become permanently fixed or flickering. In the voter model, which has no surface tension, such zealots or flickers freely spread their opinions and that makes the system disordered. For models with a surface tension, like the Ising model or the Naming Game model, their role is limited, and such systems are ordered at large z. However, when z decreases, the density of zealots or flickers increases, and below a certain threshold (z∼ 1.9-2.0 ) the system becomes disordered. On undirected random graphs, agreement dynamics is very different and ordering appears as soon the graph is above the percolation threshold at z = 1.
Approximate distance oracles for planar graphs with improved query time-space tradeoff
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2016-01-01
We consider approximate distance oracles for edge-weighted n-vertex undirected planar graphs. Given fixed ϵ > 0, we present a (1 + ϵ)-approximate distance oracle with O(n(log log n)2) space and O((loglogr?,)3) query time. This improves the previous best product of query time and space...
Undirected learning styles and academic risk: Analysis of the impact of stress, strain and coping.
Kimatian, Stephen; Lloyd, Sara; Berger, Jeffrey; Steiner, Lorraine; McKay, Robert; Schwengal, Deborah
2017-01-01
Learning style inventories used in conjunction with a measure of academic achievement consistently show an association of meaning directed learning patterns with academic success, but have failed to show a clear association of undirected learning styles with academic failure. Using survey methods with anesthesia residents, this study questioned whether additional assessment of factors related to stress, strain, and coping help to better define the association between undirected learning styles and academic risk. Pearson chi squared tests. 296 subjects were enrolled from eight institutions with 142 (48%) completing the study. American Board of Anesthesiologists In Training Examinations (ITE) percentiles (ITE%) were used as a measure of academic achievement. The Vermunt Inventory of Learning Styles (ILS) was used to identify four learning patterns and 20 strategies, and the Osipow Stress Inventory-Revised (OSI-R) was used as a measure of six scales of occupational stress, four of personal strain, and four coping resources. Two learning patterns had significant relationship with ITE scores. As seen in previous studies, Meaning Directed Learning was beneficial for academic achievement while Undirected Learning was the least beneficial. Higher scores on Meaning Directed Learning correlated positively with higher ITE scores while higher Undirected and lower Meaning Directed patterns related negatively to ITE%. OSI-R measures of stress, strain and coping indicated that residents with Undirected learning patterns had higher scores on three scales related to stress, and 4 related to strain, while displaying lower scores on two scales related to coping. Residents with higher Meaning Directed patterns scored lower on two scales of stress and two scales of strain, with higher scores on two scales for coping resources. Low Meaning Directed and high Undirected learning patterns correlated with lower ITE percentiles, higher scores for stress and strain, and lower coping resources
Gaussian covariance graph models accounting for correlated marker effects in genome-wide prediction.
Martínez, C A; Khare, K; Rahman, S; Elzo, M A
2017-10-01
Several statistical models used in genome-wide prediction assume uncorrelated marker allele substitution effects, but it is known that these effects may be correlated. In statistics, graphical models have been identified as a useful tool for covariance estimation in high-dimensional problems and it is an area that has recently experienced a great expansion. In Gaussian covariance graph models (GCovGM), the joint distribution of a set of random variables is assumed to be Gaussian and the pattern of zeros of the covariance matrix is encoded in terms of an undirected graph G. In this study, methods adapting the theory of GCovGM to genome-wide prediction were developed (Bayes GCov, Bayes GCov-KR and Bayes GCov-H). In simulated data sets, improvements in correlation between phenotypes and predicted breeding values and accuracies of predicted breeding values were found. Our models account for correlation of marker effects and permit to accommodate general structures as opposed to models proposed in previous studies, which consider spatial correlation only. In addition, they allow incorporation of biological information in the prediction process through its use when constructing graph G, and their extension to the multi-allelic loci case is straightforward. © 2017 Blackwell Verlag GmbH.
A classification of cubic symmetric graphs of order 16p2
Indian Academy of Sciences (India)
Introduction. Throughout this paper, graphs are assumed to be finite, simple, undirected and connected. For the group-theoretic concepts and notations not defined here we refer to [18]. For a graph X, we denote by V(X), E(X), A(X) and Aut(X) the vertex set, the edge set, the arc set and the full automorphism group of X, ...
Suborbital graphs of the symmetric group S n acting on unordered r ...
African Journals Online (AJOL)
In this paper we construct the suborbital graphs of the symmetric group Sn acting on unordered r‐element subsets of X = {1, 2, 3, ..., n}, χ(r) (r,n ∈ ℕ) and analyse their properties. It is shown that the suborbital graphs are undirected, connected if r <½n, and have girth three if n ≥ 3r. Key words: Symmetric group, r‐element ...
Empirical Bayes conditional independence graphs for regulatory network recovery
Mahdi, Rami; Madduri, Abishek S.; Wang, Guoqing; Strulovici-Barel, Yael; Salit, Jacqueline; Hackett, Neil R.; Crystal, Ronald G.; Mezey, Jason G.
2012-01-01
Motivation: Computational inference methods that make use of graphical models to extract regulatory networks from gene expression data can have difficulty reconstructing dense regions of a network, a consequence of both computational complexity and unreliable parameter estimation when sample size is small. As a result, identification of hub genes is of special difficulty for these methods. Methods: We present a new algorithm, Empirical Light Mutual Min (ELMM), for large network reconstruction that has properties well suited for recovery of graphs with high-degree nodes. ELMM reconstructs the undirected graph of a regulatory network using empirical Bayes conditional independence testing with a heuristic relaxation of independence constraints in dense areas of the graph. This relaxation allows only one gene of a pair with a putative relation to be aware of the network connection, an approach that is aimed at easing multiple testing problems associated with recovering densely connected structures. Results: Using in silico data, we show that ELMM has better performance than commonly used network inference algorithms including GeneNet, ARACNE, FOCI, GENIE3 and GLASSO. We also apply ELMM to reconstruct a network among 5492 genes expressed in human lung airway epithelium of healthy non-smokers, healthy smokers and individuals with chronic obstructive pulmonary disease assayed using microarrays. The analysis identifies dense sub-networks that are consistent with known regulatory relationships in the lung airway and also suggests novel hub regulatory relationships among a number of genes that play roles in oxidative stress and secretion. Availability and implementation: Software for running ELMM is made available at http://mezeylab.cb.bscb.cornell.edu/Software.aspx. Contact: ramimahdi@yahoo.com or jgm45@cornell.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22685074
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.
On the problem of finding disjoint cycles and dicycles in a digraph
DEFF Research Database (Denmark)
Bang-Jensen, Jørgen; Kriesell, M.
2011-01-01
We study the following problem: Given a digraph D, decide if there is a cycle B in D and a cycle C in its underlying undirected graph UG(D) such that V (B)a (c) V (C)=o. Whereas the problem is NP-complete if, as additional part of the input, a vertex x is prescribed to be contained in C, we prove...... methods relying on Thomassen's theorem on 2-linkages in acyclic digraphs. For the case tau (D)a parts per thousand currency sign1 we provide an algorithm independent from any earlier work.......We study the following problem: Given a digraph D, decide if there is a cycle B in D and a cycle C in its underlying undirected graph UG(D) such that V (B)a (c) V (C)=o. Whereas the problem is NP-complete if, as additional part of the input, a vertex x is prescribed to be contained in C, we prove.......e. the smallest cardinality of a set T of vertices in D such that D-T is acyclic: If tau (D)a parts per thousand yen3 then we employ McCuaig's framework on intercyclic digraphs to (always) find these cycles. If tau (D) = 2 then we can characterize the digraphs for which the answer is "yes" by using topological...
Cruz-Roa, Angel; Xu, Jun; Madabhushi, Anant
2015-01-01
Nuclear architecture or the spatial arrangement of individual cancer nuclei on histopathology images has been shown to be associated with different grades and differential risk for a number of solid tumors such as breast, prostate, and oropharyngeal. Graph-based representations of individual nuclei (nuclei representing the graph nodes) allows for mining of quantitative metrics to describe tumor morphology. These graph features can be broadly categorized into global and local depending on the type of graph construction method. While a number of local graph (e.g. Cell Cluster Graphs) and global graph (e.g. Voronoi, Delaunay Triangulation, Minimum Spanning Tree) features have been shown to associated with cancer grade, risk, and outcome for different cancer types, the sensitivity of the preceding segmentation algorithms in identifying individual nuclei can have a significant bearing on the discriminability of the resultant features. This therefore begs the question as to which features while being discriminative of cancer grade and aggressiveness are also the most resilient to the segmentation errors. These properties are particularly desirable in the context of digital pathology images, where the method of slide preparation, staining, and type of nuclear segmentation algorithm employed can all dramatically affect the quality of the nuclear graphs and corresponding features. In this paper we evaluated the trade off between discriminability and stability of both global and local graph-based features in conjunction with a few different segmentation algorithms and in the context of two different histopathology image datasets of breast cancer from whole-slide images (WSI) and tissue microarrays (TMA). Specifically in this paper we investigate a few different performance measures including stability, discriminability and stability vs discriminability trade off, all of which are based on p-values from the Kruskal-Wallis one-way analysis of variance for local and global
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.
Graph passing in graph transformation
Ghamarian, A.H.; Rensink, Arend; Fish, Andrew; Lambers, Leen
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
Graph Passing in Graph Transformation
Ghamarian, A.H.; Rensink, Arend
2012-01-01
Graph transformation works under the whole world assumption. Therefore, in realistic systems, both the individual graphs and the set of all such graphs can grow very large. In reactive formalisms such as process algebra, on the other hand, each system is split into smaller components which
Constant time distance queries in planar unweighted graphs with subquadratic preprocessing time
DEFF Research Database (Denmark)
Wulff-Nilsen, C.
2013-01-01
Let G be an n-vertex planar, undirected, and unweighted graph. It was stated as open problems whether the Wiener index, defined as the sum of all-pairs shortest path distances, and the diameter of G can be computed in o(n(2)) time. We show that both problems can be solved in O(n(2) log log n/log n......) time with O(n) space. The techniques that we apply allow us to build, within the same time bound, an oracle for exact distance queries in G. More generally, for any parameter S is an element of [(log n/log log n)(2), n(2/5)], distance queries can be answered in O (root S log S/log n) time per query...... with O(n(2)/root S) preprocessing time and space requirement. With respect to running time, this is better than previous algorithms when log S = o(log n). All algorithms have linear space requirement. Our results generalize to a larger class of graphs including those with a fixed excluded minor. (C) 2012...
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
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.
On the Optimization and Parallelizing Little Algorithm for Solving the Traveling Salesman Problem
Directory of Open Access Journals (Sweden)
V. V. Vasilchikov
2016-01-01
Full Text Available The paper describes some ways to accelerate solving the NP-complete Traveling Salesman Problem. The classic Little algorithm belonging to the category of ”branch and bound methods” can solve it both for directed and undirected graphs. However, for undirected graphs its operation can be accelerated by eliminating the consideration of branches examined earlier. The paper proposes changes to be made in the key operations of the algorithm to speed up its execution. It also describes the results of an experiment that demonstrated a significant acceleration of solving the problem by using an advanced algorithm. Another way to speed up the work is to parallelize the algorithm. For problems of this kind it is difficult to break the task into a sufficient number of subtasks having comparable complexity. Their parallelism arises dynamically during the execution. For such problems, it seems reasonable to use parallel-recursive algorithms. In our case the use of the library RPM ParLib developed by the author was a good choice. It allows us to develop effective applications for parallel computing on a local network using any .NET-compatible programming language. We used C# to develop the programs. Parallel applications were developed as for basic and modified algorithms, the comparing of their speed was made. Experiments were performed for the graphs with the number of vertexes up to 45 and with the number of network computers up to 16. We also investigated the acceleration that can be achieved by parallelizing the basic Little algorithm for directed graphs. The results of these experiments are also presented in the paper.
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
Penafiel, Carlos
2014-01-01
In this paper we find functions over bounded domains in the 2-dimensional Euclidean space, whose graphs (in the Heisenberg space) has constant mean curvature different from zero and taking on (possibly) infinite boundary values over the boundary of the domain.
On P-transitive graphs and applications
Directory of Open Access Journals (Sweden)
Giacomo Lenzi
2011-06-01
Full Text Available We introduce a new class of graphs which we call P-transitive graphs, lying between transitive and 3-transitive graphs. First we show that the analogue of de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we show that the mu-calculus fixpoint hierarchy is infinite for P-transitive graphs. Both results contrast with the case of transitive graphs. We give also an undecidability result for an enriched mu-calculus on P-transitive graphs. Finally, we consider a polynomial time reduction from the model checking problem on arbitrary graphs to the model checking problem on P-transitive graphs. All these results carry over to 3-transitive graphs.
Chordal Graphs and Semidefinite Optimization
DEFF Research Database (Denmark)
Vandenberghe, Lieven; Andersen, Martin Skovgaard
2015-01-01
Chordal graphs play a central role in techniques for exploiting sparsity in large semidefinite optimization problems and in related con-vex optimization problems involving sparse positive semidefinite matrices. Chordal graph properties are also fundamental to several classical results in combinat...
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Convergence speed of consensus problems over undirected scale-free networks
International Nuclear Information System (INIS)
Sun Wei; Dou Li-Hua
2010-01-01
Scale-free networks and consensus behaviour among multiple agents have both attracted much attention. To investigate the consensus speed over scale-free networks is the major topic of the present work. A novel method is developed to construct scale-free networks due to their remarkable power-law degree distributions, while preserving the diversity of network topologies. The time cost or iterations for networks to reach a certain level of consensus is discussed, considering the influence from power-law parameters. They are both demonstrated to be reversed power-law functions of the algebraic connectivity, which is viewed as a measurement on convergence speed of the consensus behaviour. The attempts of tuning power-law parameters may speed up the consensus procedure, but it could also make the network less robust over time delay at the same time. Large scale of simulations are supportive to the conclusions. (general)
Gusfield, Dan
2010-03-01
The Multi-State Perfect Phylogeny Problem is an extension of the Binary Perfect Phylogeny Problem, allowing characters to take on more than two states. In this article, we consider three problems that extend the utility of the multi-state perfect phylogeny model: (1) the Missing Data (MD) Problem, where some entries in the input are missing and the question is whether (bounded) values for the missing data can be imputed so that the resulting data has a multi-state perfect phylogeny; (2) the Character-Removal (CR) Problem, where we want to minimize the number of characters to remove from the data so that the resulting data has a multi-state perfect phylogeny; and (3) the Missing-Data Character-Removal (MDCR) Problem, where the input has missing data and we want to impute values for the missing data to minimize the solution to the resulting Character-Removal Problem. We discuss Integer Linear Programming (ILP) solutions to these problems for the special case of three, four, and five permitted states per character, and we report on extensive empirical testing of these solutions. Then we develop a general theory to solve the MD problem for an arbitrary number of permitted states, using chordal graph theory and results on minimal triangulation of non-chordal graphs. This establishes new necessary and sufficient conditions for the existence of a perfect phylogeny with (or without) missing data. We implement the general theory using integer linear programming, although other optimization methods are possible. We extensively explore the empirical behavior of the general solution, showing that the methods are very practical for data of size and complexity that is characteristic of many current applications in phylogenetics. Some of the empirical results for the MD problem with an arbitrary number of permitted states are very surprising, suggesting the existence of additional combinatorial structure in multi-state perfect phylogenies. Finally, we note some relationships
Bogiatzis, P.; Ishii, M.; Davis, T. A.
2016-12-01
Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. We show how combinatorics and graph theory can be used to analyze the structure of such problems, and to effectively decompose them into smaller ones that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. Furthermore, we show that a new sparse singular value decomposition method can be used to obtain the complete spectrum of the singular values. This procedure provides the means for more objective regularization and further dimensionality reduction of the problem. We apply this methodology to a moderate size, non-linear seismic tomography problem to image the structure of the crust and the upper mantle beneath Japan using local deep earthquakes recorded by the High Sensitivity Seismograph Network stations.
DEFF Research Database (Denmark)
Tegos, Stergios; Demetriadis, Stavros N.; Papadopoulos, Pantelis M.
2016-01-01
Conversational agents that draw on the framework of academically productive talk (APT) have been lately shown to be effective in helping learners sustain productive forms of peer dialogue in diverse learning settings. Yet, literature suggests that more research is required on how learners respond...... instead of the dyad (D treatment). The results suggest that although both agent intervention methods can improve students’ learning outcomes and dyad in-task performance, the directed one is more effective than the undirected one in enhancing individual domain knowledge acquisition and explicit reasoning....... Furthermore, findings show that the positive effect of the agent on dyad performance is mediated by the frequency of students’ contributions displaying explicit reasoning, while most students perceive agent involvement favorably....
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''''.
Directory of Open Access Journals (Sweden)
Stefania Casagrande
2016-10-01
Full Text Available Song is a sexually selected trait that is thought to be an honest signal of the health condition of an individual in many bird species. For species that breed opportunistically, the quantity of food may be a determinant of singing activity. However, it is not yet known whether the quality of food plays an important role in this respect. The aim of the present study was to experimentally investigate the role of two calorie-free nutrients (lutein and cholesterol in determining the expression of a sexually selected behavior (song rate and other behaviors (locomotor activity, self-maintenance activity, eating and resting in male zebra finches (Taeniopygia guttata. We predicted that males supplemented with lutein and cholesterol would sing at higher rates than controls because both lutein and cholesterol have important health-related physiological functions in birds and birdsong mirrors individual condition. To control for testosterone secretion that may upregulate birdsong, birds were exposed to a decreasing photoperiod. Our results showed that control males down-regulated testosterone in response to a decreasing photoperiod, while birds treated with lutein or cholesterol maintained a constant singing activity. Both lutein- and cholesterol-supplemented groups sang more than control groups by the end of the experiment, indicating that the quality of food can affect undirected song irrespective of circulating testosterone concentrations. None of the other measured behaviors were affected by the treatment, suggesting that, when individuals have full availability of food, sexually selected song traits are more sensitive to the effect of food quality than other behavioral traits. Overall the results support our prediction that undirected song produced by male zebra finches signals access to high-quality food.
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....... Despite this, we are able to develop betweenness reconstruction algorithms that match the current state of the art for distance reconstruction, and even improve it for certain types of graphs. We obtain the following algorithms: 1. Reconstruction of general graphs in O(n2) queries 2. Reconstruction...... of degree-bounded graphs in Õ(n3/2) queries 3. Reconstruction of geodetic degree-bounded graphs in Õ(n) queries In addition to being a fundamental graph theoretic problem with some natural applications, our new results shed light on some avenues for progress in the distance reconstruction problem....
Spectral partitioning in equitable graphs.
Barucca, Paolo
2017-06-01
Graph partitioning problems emerge in a wide variety of complex systems, ranging from biology to finance, but can be rigorously analyzed and solved only for a few graph ensembles. Here, an ensemble of equitable graphs, i.e., random graphs with a block-regular structure, is studied, for which analytical results can be obtained. In particular, the spectral density of this ensemble is computed exactly for a modular and bipartite structure. Kesten-McKay's law for random regular graphs is found analytically to apply also for modular and bipartite structures when blocks are homogeneous. An exact solution to graph partitioning for two equal-sized communities is proposed and verified numerically, and a conjecture on the absence of an efficient recovery detectability transition in equitable graphs is suggested. A final discussion summarizes results and outlines their relevance for the solution of graph partitioning problems in other graph ensembles, in particular for the study of detectability thresholds and resolution limits in stochastic block models.
Zhou, Feng; de la Torre, Fernando
2015-11-19
Graph matching (GM) is a fundamental problem in computer science, and it plays a central role to solve correspondence problems in computer vision. GM problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem (QAP). Although widely used, solving the correspondence problem through GM has two main limitations: (1) the QAP is NP-hard and difficult to approximate; (2) GM algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems. To address aforementioned problems, this paper proposes factorized graph matching (FGM). FGM factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges. Four are the benefits that follow from this factorization: (1) There is no need to compute the costly (in space and time) pairwise affinity matrix; (2) The factorization allows the use of a path-following optimization algorithm, that leads to improved optimization strategies and matching performance; (3) Given the factorization, it becomes straight-forward to incorporate geometric transformations (rigid and non-rigid) to the GM problem. (4) Using a matrix formulation for the GM problem and the factorization, it is easy to reveal commonalities and differences between different GM methods. The factorization also provides a clean connection with other matching algorithms such as iterative closest point; Experimental results on synthetic and real databases illustrate how FGM outperforms state-of-the-art algorithms for GM. The code is available at http://humansensing.cs.cmu.edu/fgm.
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
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
2012-11-19
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.
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...
The fascinating world of graph theory
Benjamin, Arthur; Zhang, Ping
2015-01-01
Graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducin
Girth 5 graphs from relative difference sets
DEFF Research Database (Denmark)
Jørgensen, Leif Kjær
We consider the problem of construction of graphs with given degree and girth 5 and as few vertices as possible. We give a construction of a family of girth 5 graphs based on relative difference sets. This family contains the smallest known graph of degree 8 and girth 5 which was constructed by G...
A minimum resource neural network framework for solving multiconstraint shortest path problems.
Zhang, Junying; Zhao, Xiaoxue; He, Xiaotao
2014-08-01
Characterized by using minimum hard (structural) and soft (computational) resources, a novel parameter-free minimal resource neural network (MRNN) framework is proposed for solving a wide range of single-source shortest path (SP) problems for various graph types. The problems are the k-shortest time path problems with any combination of three constraints: time, hop, and label constraints, and the graphs can be directed, undirected, or bidirected with symmetric and/or asymmetric traversal time, which can be real and time dependent. Isomorphic to the graph where the SP is to be sought, the network is activated by generating autowave at source neuron and the autowave travels automatically along the paths with the speed of a hop in an iteration. Properties of the network are studied, algorithms are presented, and computation complexity is analyzed. The framework guarantees globally optimal solutions of a series of problems during the iteration process of the network, which provides insight into why even the SP is still too long to be satisfied. The network facilitates very large scale integrated circuit implementation and adapt to very large scale problems due to its massively parallel processing and minimum resource utilization. When implemented in a sequentially processing computer, experiments on synthetic graphs, road maps of cities of the USA, and vehicle routing with time windows indicate that the MRNN is especially efficient for large scale sparse graphs and even dense graphs with some constraints, e.g., the CPU time taken and the iteration number used for the road maps of cities of the USA is even less than ∼ 2% and 0.5% that of the Dijkstra's algorithm.
A Super (A,D-Bm-Antimagic Total Covering of Ageneralized Amalgamation of Fan Graphs
Directory of Open Access Journals (Sweden)
Ika Hesti Agustin
2017-05-01
Full Text Available All graph in this paper are finite, simple and undirected. Let G, H be two graphs. A graph G is said to be an (a,d-H-antimagic total graph if there exist a bijective function such that for all subgraphs H’ isomorphic to H, the total H-weights form an arithmetic progression where a, d > 0 are integers and m is the number of all subgraphs H’ isomorphic to H. An (a, d-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study a super (a, d-Bm-antimagicness of a connected and disconnected generalized amalgamation of fan graphs on which a path is a terminal.
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...
Graph theory and combinatorial optimization
Marcotte, Odile; Avis, David
2006-01-01
A current treatment of cutting-edge topics in Graph Theory and Combinatorial Optimization by leading researchersIncludes heuristic advances and novel approaches to solving combinatorial optimization problems.
Subgraph Enumeration in Massive Graphs
DEFF Research Database (Denmark)
Silvestri, Francesco
We consider the problem of enumerating all instances of a given sample graph in a large data graph. Our focus is on determining the input/output (I/O) complexity of this problem. Let $E$ be the number of edges in the data graph, $k=\\BO{1}$ be the number of vertexes in the sample graph, $B......$ be the block length, and $M$ be the main memory size. The main result of the paper is a randomized algorithm that enumerates all instances of the sample graph in $\\BO{E^{k/2}/\\left(BM^{k/2-1}\\right)}$ expected I/Os if the maximum vertex degree of the data graph is $\\sqrt{EM}$. Under some assumptions, the same...... bound also applies with high probability. Our algorithm is I/O optimal, in the worst-case, when the sample graph belongs to the Alon class, which includes cliques, cycles and every graph with a perfect matching: indeed, we show that any algorithm enumerating $T$ instances must always use $\\BOM...
Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs
R.C. Laskar (R.C.); H.M. Mulder (Martyn); B. Novick (Beth)
2011-01-01
textabstractMaximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices, two of these being adjacent
Graphs Theory and Applications
Fournier, Jean-Claude
2008-01-01
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the
Al Nasr, Kamal; Ranjan, Desh; Zubair, Mohammad; Chen, Lin; He, Jing
2014-01-01
Electron cryomicroscopy is becoming a major experimental technique in solving the structures of large molecular assemblies. More and more three-dimensional images have been obtained at the medium resolutions between 5 and 10 Å. At this resolution range, major α-helices can be detected as cylindrical sticks and β-sheets can be detected as plain-like regions. A critical question in de novo modeling from cryo-EM images is to determine the match between the detected secondary structures from the image and those on the protein sequence. We formulate this matching problem into a constrained graph problem and present an O(Δ(2)N(2)2(N)) algorithm to this NP-Hard problem. The algorithm incorporates the dynamic programming approach into a constrained K-shortest path algorithm. Our method, DP-TOSS, has been tested using α-proteins with maximum 33 helices and α-β proteins up to five helices and 12 β-strands. The correct match was ranked within the top 35 for 19 of the 20 α-proteins and all nine α-β proteins tested. The results demonstrate that DP-TOSS improves accuracy, time and memory space in deriving the topologies of the secondary structure elements for proteins with a large number of secondary structures and a complex skeleton.
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...
CHARACTERISATION OF REGULAR GRAPHS AS LOOP GRAPHS ...
African Journals Online (AJOL)
There have been various generalisations of Cayley graphs, prototypes of transitive graphs. The most generalised is the description of graphs on general groupoids. What has clearly emerged in this exercise is that the philosophy of constructing graphs on groupoids offers a fruitful avenue from which we may understand ...
2010-12-02
evaluating the function ΘP (A) for any fixed A,P is equivalent to solving the so-called Quadratic Assignment Problem ( QAP ), and thus we can employ various...tractable linear programming, spectral, and SDP relaxations of QAP [40, 11, 33]. In particular we discuss recent work [14] on exploiting group...symmetry in SDP relaxations of QAP , which is useful for approximately computing elementary convex graph invariants in many interesting cases. Finally in
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin 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 graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
SOUR graphs for efficient completion
Lynch, Christopher; Strogova, Polina
1998-01-01
International audience; We introduce a data structure called \\emphSOUR graphs and present an efficient Knuth-Bendix completion procedure based on it. \\emphSOUR graphs allow for a maximal structure sharing of terms in rewriting systems. The term representation is a dag representation, except that edges are labelled with equational constraints and variable renamings. The rewrite rules correspond to rewrite edges, the unification problems to unification edges. The Critical Pair and Simplificatio...
Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs
Directory of Open Access Journals (Sweden)
Hala Kamal
2017-11-01
Full Text Available Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach.
Graph limits and hereditary properties
Janson, Svante
2011-01-01
We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs, chordal graphs, cographs, interval graphs, unit interval graphs, threshold graphs, and line graphs.
Algorithms for Planar Graphs and Graphs in Metric Spaces
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...... a graph with new edges while minimizing stretch factor. The third and final part of the thesis deals with the Steiner tree problem in the plane equipped with a weighted fixed orientation metric. Here, we give an improved theoretical analysis of the strength of pruning techniques applied by many Steiner...
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.
Exact numerical calculation of fixation probability and time on graphs.
Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt
2016-12-01
The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Quantum centrality testing on directed graphs via P T -symmetric quantum walks
Izaac, J. A.; Wang, J. B.; Abbott, P. C.; Ma, X. S.
2017-09-01
Various quantum-walk-based algorithms have been proposed to analyze and rank the centrality of graph vertices. However, issues arise when working with directed graphs: the resulting non-Hermitian Hamiltonian leads to nonunitary dynamics, and the total probability of the quantum walker is no longer conserved. In this paper, we discuss a method for simulating directed graphs using P T -symmetric quantum walks, allowing probability-conserving nonunitary evolution. This method is equivalent to mapping the directed graph to an undirected, yet weighted, complete graph over the same vertex set, and can be extended to cover interdependent networks of directed graphs. Previous work has shown centrality measures based on the continuous-time quantum walk provide an eigenvectorlike quantum centrality; using the P T -symmetric framework, we extend these centrality algorithms to directed graphs with a significantly reduced Hilbert space compared to previous proposals. In certain cases, this centrality measure provides an advantage over classical algorithms used in network analysis, for example, by breaking vertex rank degeneracy. Finally, we perform a statistical analysis over ensembles of random graphs, and show strong agreement with the classical PageRank measure on directed acyclic graphs.
On Rainbow k-Connection Number of Special Graphs and It’s Sharp Lower Bound
Hesti Agustin, Ika; Dafik; Gembong, A. W.; Alfarisi, Ridho
2017-06-01
Let G = (V, E) be a simple, nontrivial, finite, connected and undirected graph. Let c be a coloring c : E(G) → {1, 2, …, s}, s ∈ N. A path of edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph G is said to be a rainbow connected graph if there exists a rainbow u - v path for every two vertices u and v of G. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of k colors required to edge color the graph such that the graph is rainbow connected. Furthermore, for an l-connected graph G and an integer k with 1 ≤ k ≤ l, the rainbow k-connection number rck (G) of G is defined to be the minimum number of colors required to color the edges of G such that every two distinct vertices of G are connected by at least k internally disjoint rainbow paths. In this paper, we determine the exact values of rainbow connection number of some special graphs and obtain a sharp lower bound.
Triangle Counting in Dynamic Graph Streams
DEFF Research Database (Denmark)
Bulteau, Laurent; Froese, Vincent; Pagh, Rasmus
2015-01-01
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However......, with a few exceptions, the algorithms have considered insert-only streams. We present a new algorithm estimating the number of triangles in dynamic graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions...... for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach...
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
Dynamic Programming on Nominal Graphs
Directory of Open Access Journals (Sweden)
Nicklas Hoch
2015-04-01
Full Text Available Many optimization problems can be naturally represented as (hyper graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.
A contribution to queens graphs
DEFF Research Database (Denmark)
Barat, Janos
A graph $G$ is a queens graph if the vertices of $G$ can be mapped to queens on the chessboard such that two vertices are adjacent if and only if the corresponding queens attack each other, i.e. they are in horizontal, vertical or diagonal position. We prove a conjecture of Beineke, Broere...... and Henning that the Cartesian product of an odd cycle and a path is a queens graph. We show that the same does not hold for two odd cycles. % is not representable in the same way. The representation of the Cartesian product of an odd cycle and an even cycle remains an open problem. We also prove...... constructively that any finite subgraph of the grid or the hexagonal grid is a queens graph....
Components in time-varying graphs.
Nicosia, Vincenzo; Tang, John; Musolesi, Mirco; Russo, Giovanni; Mascolo, Cecilia; Latora, Vito
2012-06-01
Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.
A survey of results on integral trees and integral graphs
Wang, Ligong
2005-01-01
A graph $G$ is called {\\it integral} if all zeros of the characteristic polynomial $P(G,x)$ are integers. Our purpose is to determine or to characterize which graphs are integral. This problem was posed by Harary and Schwenk in 1974. In general, the problem of characterizing integral graphs seems to
Genus Zero Graph Segmentation: Estimation of Intracranial Volume
DEFF Research Database (Denmark)
Jensen, Rasmus Ramsbøl; Thorup, Signe Strann; Paulsen, Rasmus Reinhold
2013-01-01
present a fully automatic 3D graph-based method for segmentation of the ICV in non-contrast CT scans. We reformulate the ICV segmentation problem as an optimal genus 0 segmentation problem in a volumetric graph. The graph is the result of a volumetric spherical subsample from the data connected using...
Graph coarsening and clustering on the GPU
Fagginger Auer, B.O.; Bisseling, R.H.
2013-01-01
Agglomerative clustering is an effective greedy way to quickly generate graph clusterings of high modularity in a small amount of time. In an effort to use the power offered by multi-core CPU and GPU hardware to solve the clustering problem, we introduce a fine-grained sharedmemory parallel graph
Toughness and Triangle-Free Graphs
Bauer, D.; van den Heuvel, J.; Schmeichel, E.
1995-01-01
In this paper, we prove that there exist triangle-free graphs with arbitrarily large toughness, thereby settling a longstanding open question. We also explore the problem of whether there exists a t-tough, n/(t + 1)-regular, triangle-free graph on n vertices for various values of t, and provide a
On the centrality of vertices of molecular graphs.
Randić, Milan; Novič, Marjana; Vračko, Marjan; Plavšić, Dejan
2013-11-05
For acyclic systems the center of a graph has been known to be either a single vertex of two adjacent vertices, that is, an edge. It has not been quite clear how to extend the concept of graph center to polycyclic systems. Several approaches to the graph center of molecular graphs of polycyclic graphs have been proposed in the literature. In most cases alternative approaches, however, while being apparently equally plausible, gave the same results for many molecules, but occasionally they differ in their characterization of molecular center. In order to reduce the number of vertices that would qualify as forming the center of the graph, a hierarchy of rules have been considered in the search for graph centers. We reconsidered the problem of "the center of a graph" by using a novel concept of graph theory, the vertex "weights," defined by counting the number of pairs of vertices at the same distance from the vertex considered. This approach gives often the same results for graph centers of acyclic graphs as the standard definition of graph center based on vertex eccentricities. However, in some cases when two nonequivalent vertices have been found as graph center, the novel approach can discriminate between the two. The same approach applies to cyclic graphs without additional rules to locate the vertex or vertices forming the center of polycyclic graphs, vertices referred to as central vertices of a graph. In addition, the novel vertex "weights," in the case of acyclic, cyclic, and polycyclic graphs can be interpreted as vertex centralities, a measure for how close or distant vertices are from the center or central vertices of the graph. Besides illustrating the centralities of a number of smaller polycyclic graphs, we also report on several acyclic graphs showing the same centrality values of their vertices. Copyright © 2013 Wiley Periodicals, Inc.
Fixation Time for Evolutionary Graphs
Nie, Pu-Yan; Zhang, Pei-Ai
Evolutionary graph theory (EGT) is recently proposed by Lieberman et al. in 2005. EGT is successful for explaining biological evolution and some social phenomena. It is extremely important to consider the time of fixation for EGT in many practical problems, including evolutionary theory and the evolution of cooperation. This study characterizes the time to asymptotically reach fixation.
Acyclicity in edge-colored graphs
DEFF Research Database (Denmark)
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type i......+1, i=1,2,3,4. The first three types are equivalent to the absence of PC cycles, PC closed trails, and PC closed walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored...... graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex...
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
Directory of Open Access Journals (Sweden)
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
Algorithms for Graph Rigidity and Scene Analysis
DEFF Research Database (Denmark)
Berg, Alex Rune; Jordán, Tibor
2003-01-01
We investigate algorithmic questions and structural problems concerning graph families defined by `edge-counts'. Motivated by recent developments in the unique realization problem of graphs, we give an efficient algorithm to compute the rigid, redundantly rigid, M-connected, and globally rigid...... components of a graph. Our algorithm is based on (and also extends and simplifies) the idea of Hendrickson and Jacobs, as it uses orientations as the main algorithmic tool. We also consider families of bipartite graphs which occur in parallel drawings and scene analysis. We verify a conjecture of Whiteley...... by showing that 2d-connected bipartite graphs are d-tight. We give a new algorithm for finding a maximal d-sharp subgraph. We also answer a question of Imai and show that finding a maximum size d-sharp subgraph is NP-hard....
On the partition dimension of two-component graphs
Indian Academy of Sciences (India)
D O Haryeni
2017-11-17
Nov 17, 2017 ... Partition dimension; disconnected graph; component. 2010 Mathematics Subject Classification. 05C12, 05C15. 1. Introduction. The study of the partition dimension for graphs was initiated by Chartrand et al. [2] aimed at finding a new way to solve the problem in metric dimensions of graphs. Many results.
Mutual proximity graphs for improved reachability in music recommendation.
Flexer, Arthur; Stevens, Jeff
2018-01-01
This paper is concerned with the impact of hubness, a general problem of machine learning in high-dimensional spaces, on a real-world music recommendation system based on visualisation of a k-nearest neighbour (knn) graph. Due to a problem of measuring distances in high dimensions, hub objects are recommended over and over again while anti-hubs are nonexistent in recommendation lists, resulting in poor reachability of the music catalogue. We present mutual proximity graphs, which are an alternative to knn and mutual knn graphs, and are able to avoid hub vertices having abnormally high connectivity. We show that mutual proximity graphs yield much better graph connectivity resulting in improved reachability compared to knn graphs, mutual knn graphs and mutual knn graphs enhanced with minimum spanning trees, while simultaneously reducing the negative effects of hubness.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
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.
An integer programming formulation of the parsimonious loss of heterozygosity problem.
Catanzaro, Daniele; Labbé, Martine; Halldórsson, Bjarni V
2013-01-01
A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches.
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....
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.
Graphs on Surfaces and the Partition Function of String Theory
Garcia-Islas, J. Manuel
2007-01-01
Graphs on surfaces is an active topic of pure mathematics belonging to graph theory. It has also been applied to physics and relates discrete and continuous mathematics. In this paper we present a formal mathematical description of the relation between graph theory and the mathematical physics of discrete string theory. In this description we present problems of the combinatorial world of real importance for graph theorists. The mathematical details of the paper are as follows: There is a com...
Directory of Open Access Journals (Sweden)
Chuan Yan
2014-01-01
Full Text Available This paper mainly investigates the event-triggered control for discrete-time multiagent systems with the problem of packet losses and communication delays when both the first-order and the second-order neighbors’ information are used. Event-triggered control laws are adopted so as to reduce the frequency of individual actuation updating under the sampled-data framework for discrete-time agent dynamics. The communication graph is undirected and the loss of data across each communication link occurs at certain probability, which is governed by a Bernoulli process. It is found that the distributed consensus speeds up by using the second-order neighbors’ information when packet losses and communication delays occur. Numerical examples are given to demonstrate the effectiveness of the proposed methods.
Discriminative graph embedding for label propagation.
Nguyen, Canh Hao; Mamitsuka, Hiroshi
2011-09-01
In many applications, the available information is encoded in graph structures. This is a common problem in biological networks, social networks, web communities and document citations. We investigate the problem of classifying nodes' labels on a similarity graph given only a graph structure on the nodes. Conventional machine learning methods usually require data to reside in some Euclidean spaces or to have a kernel representation. Applying these methods to nodes on graphs would require embedding the graphs into these spaces. By embedding and then learning the nodes on graphs, most methods are either flexible with different learning objectives or efficient enough for large scale applications. We propose a method to embed a graph into a feature space for a discriminative purpose. Our idea is to include label information into the embedding process, making the space representation tailored to the task. We design embedding objective functions that the following learning formulations become spectral transforms. We then reformulate these spectral transforms into multiple kernel learning problems. Our method, while being tailored to the discriminative tasks, is efficient and can scale to massive data sets. We show the need of discriminative embedding on some simulations. Applying to biological network problems, our method is shown to outperform baselines.
Integral trees and integral graphs
Wang, Ligong
2005-01-01
This monograph deals with integral graphs, Laplacian integral regular graphs, cospectral graphs and cospectral integral graphs. The organization of this work, which consists of eight chapters, is as follows.
Loukas, A.
2015-01-01
We have recently seen a surge of research focusing on the processing of graph data. The emerging field of signal processing on graphs focuses on the extension of classical discrete signal processing techniques to the graph setting. Arguably, the greatest breakthrough of the field has been the
Indian Academy of Sciences (India)
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graph. We also note before closing this general discus- sion that among the family of regular and connected graphs, the graphs in the family of SRGs are character- ized by having exactly three distinct eigenvalues of the adjacency matrix. The friendship theorem asserts that if friendship in a community is a symmetric relation ...
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
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…
Pluhař, Z; Weidenmüller, H A
2014-04-11
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.
Hyperbolicity in median graphs
Indian Academy of Sciences (India)
If is hyperbolic, we denote by () the sharp hyperbolicity constant of , i.e., ( X ) = inf { ≥ 0 : X is − hyperbolic } . In this paper we study the hyperbolicity of median graphs and we also obtain some results about general hyperbolic graphs. In particular, we prove that a median graph is hyperbolic if and only if its ...
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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%.
Gross, Jonathan L
2003-01-01
The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approaches as well as ""pure"" graph theory. They then carefully edited the compilation to produce a unified, authoritative work ideal for ready reference.Designed and edited with non-experts in mind, the Handbook of Graph Theory makes information easy to fi
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
Wong, Pak C.; Mackey, Patrick S.; Perrine, Kenneth A.; Foote, Harlan P.; Thomas, James J.
2008-12-23
Methods for visualizing a graph by automatically drawing elements of the graph as labels are disclosed. In one embodiment, the method comprises receiving node information and edge information from an input device and/or communication interface, constructing a graph layout based at least in part on that information, wherein the edges are automatically drawn as labels, and displaying the graph on a display device according to the graph layout. In some embodiments, the nodes are automatically drawn as labels instead of, or in addition to, the label-edges.
Pristine transfinite graphs and permissive electrical networks
Zemanian, Armen H
2001-01-01
A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional g...
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Enabling Graph Appliance for Genome Assembly
Energy Technology Data Exchange (ETDEWEB)
Singh, Rina [ORNL; Graves, Jeffrey A [ORNL; Lee, Sangkeun (Matt) [ORNL; Sukumar, Sreenivas R [ORNL; Shankar, Mallikarjun [ORNL
2015-01-01
In recent years, there has been a huge growth in the amount of genomic data available as reads generated from various genome sequencers. The number of reads generated can be huge, ranging from hundreds to billions of nucleotide, each varying in size. Assembling such large amounts of data is one of the challenging computational problems for both biomedical and data scientists. Most of the genome assemblers developed have used de Bruijn graph techniques. A de Bruijn graph represents a collection of read sequences by billions of vertices and edges, which require large amounts of memory and computational power to store and process. This is the major drawback to de Bruijn graph assembly. Massively parallel, multi-threaded, shared memory systems can be leveraged to overcome some of these issues. The objective of our research is to investigate the feasibility and scalability issues of de Bruijn graph assembly on Cray s Urika-GD system; Urika-GD is a high performance graph appliance with a large shared memory and massively multithreaded custom processor designed for executing SPARQL queries over large-scale RDF data sets. However, to the best of our knowledge, there is no research on representing a de Bruijn graph as an RDF graph or finding Eulerian paths in RDF graphs using SPARQL for potential genome discovery. In this paper, we address the issues involved in representing a de Bruin graphs as RDF graphs and propose an iterative querying approach for finding Eulerian paths in large RDF graphs. We evaluate the performance of our implementation on real world ebola genome datasets and illustrate how genome assembly can be accomplished with Urika-GD using iterative SPARQL queries.
Ranking graph edges by the weight of their spanning arborescences or trees
Directory of Open Access Journals (Sweden)
Paulo Oswaldo Boaventura-Netto
2008-04-01
Full Text Available A result based on a classic theorem of graph theory is generalized for edge-valued graphs, allowing determination of the total value of the spanning arborescences with a given root and containing a given arc in a directed valued graph. A corresponding result for undirected valued graphs is also presented. In both cases, the technique allows for a ranking of the graph edges by importance under this criterion. This ranking is proposed as a tool to determine the relative importance of the edges of a graph in network vulnerability studies. Some examples of application are presented.Um resultado baseado em um teorema clássico da teoria dos grafos é aqui generalizado para grafos valorados, permitindo a determinação do valor total das arborescências parciais com raiz dada que contenham um arco dado, em um grafo orientado valorado. Um resultado correspondente para grafos não orientados valorados é também apresentado. Em ambos os casos, a técnica descrita permite uma hierarquização por importância das ligações do grafo, sob este critério. Esta hierarquização é proposta como uma ferramenta para determinar a importância relativa das ligações de um grafo em estudos sobre vulnerabilidade de redes. Alguns exemplos aplicados são apresentados.
Efficient dynamic graph construction for inductive semi-supervised learning.
Dornaika, F; Dahbi, R; Bosaghzadeh, A; Ruichek, Y
2017-10-01
Most of graph construction techniques assume a transductive setting in which the whole data collection is available at construction time. Addressing graph construction for inductive setting, in which data are coming sequentially, has received much less attention. For inductive settings, constructing the graph from scratch can be very time consuming. This paper introduces a generic framework that is able to make any graph construction method incremental. This framework yields an efficient and dynamic graph construction method that adds new samples (labeled or unlabeled) to a previously constructed graph. As a case study, we use the recently proposed Two Phase Weighted Regularized Least Square (TPWRLS) graph construction method. The paper has two main contributions. First, we use the TPWRLS coding scheme to represent new sample(s) with respect to an existing database. The representative coefficients are then used to update the graph affinity matrix. The proposed method not only appends the new samples to the graph but also updates the whole graph structure by discovering which nodes are affected by the introduction of new samples and by updating their edge weights. The second contribution of the article is the application of the proposed framework to the problem of graph-based label propagation using multiple observations for vision-based recognition tasks. Experiments on several image databases show that, without any significant loss in the accuracy of the final classification, the proposed dynamic graph construction is more efficient than the batch graph construction. Copyright © 2017 Elsevier Ltd. All rights reserved.
Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult
Broersma, Haitze J.; Fomin, F.V.; Kratochvil, J.; Woeginger, Gerhard
2003-01-01
We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem.
African Journals Online (AJOL)
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. Eulerian graphs uses two of the techniques commonly employed for travelling salesman problem (TSP). In the case of undirected graphs, the problem is formulated as an integer linear programming typically containing a large constraint set.
PuLP/XtraPuLP : Partitioning Tools for Extreme-Scale Graphs
Energy Technology Data Exchange (ETDEWEB)
2017-09-21
PuLP/XtraPulp is software for partitioning graphs from several real-world problems. Graphs occur in several places in real world from road networks, social networks and scientific simulations. For efficient parallel processing these graphs have to be partitioned (split) with respect to metrics such as computation and communication costs. Our software allows such partitioning for massive graphs.
Pathfinder: Visual Analysis of Paths in Graphs
Partl, C.; Gratzl, S.; Streit, M.; Wassermann, A. M.; Pfister, H.; Schmalstieg, D.; Lex, A.
2016-01-01
The analysis of paths in graphs is highly relevant in many domains. Typically, path-related tasks are performed in node-link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path-related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder (Figure 1), a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node-link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node-link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways. PMID:27942090
Pathfinder: Visual Analysis of Paths in Graphs.
Partl, C; Gratzl, S; Streit, M; Wassermann, A M; Pfister, H; Schmalstieg, D; Lex, A
2016-06-01
The analysis of paths in graphs is highly relevant in many domains. Typically, path-related tasks are performed in node-link layouts. Unfortunately, graph layouts often do not scale to the size of many real world networks. Also, many networks are multivariate, i.e., contain rich attribute sets associated with the nodes and edges. These attributes are often critical in judging paths, but directly visualizing attributes in a graph layout exacerbates the scalability problem. In this paper, we present visual analysis solutions dedicated to path-related tasks in large and highly multivariate graphs. We show that by focusing on paths, we can address the scalability problem of multivariate graph visualization, equipping analysts with a powerful tool to explore large graphs. We introduce Pathfinder (Figure 1), a technique that provides visual methods to query paths, while considering various constraints. The resulting set of paths is visualized in both a ranked list and as a node-link diagram. For the paths in the list, we display rich attribute data associated with nodes and edges, and the node-link diagram provides topological context. The paths can be ranked based on topological properties, such as path length or average node degree, and scores derived from attribute data. Pathfinder is designed to scale to graphs with tens of thousands of nodes and edges by employing strategies such as incremental query results. We demonstrate Pathfinder's fitness for use in scenarios with data from a coauthor network and biological pathways.
Graph Embedded Extreme Learning Machine.
Iosifidis, Alexandros; Tefas, Anastasios; Pitas, Ioannis
2016-01-01
In this paper, we propose a novel extension of the extreme learning machine (ELM) algorithm for single-hidden layer feedforward neural network training that is able to incorporate subspace learning (SL) criteria on the optimization process followed for the calculation of the network's output weights. The proposed graph embedded ELM (GEELM) algorithm is able to naturally exploit both intrinsic and penalty SL criteria that have been (or will be) designed under the graph embedding framework. In addition, we extend the proposed GEELM algorithm in order to be able to exploit SL criteria in arbitrary (even infinite) dimensional ELM spaces. We evaluate the proposed approach on eight standard classification problems and nine publicly available datasets designed for three problems related to human behavior analysis, i.e., the recognition of human face, facial expression, and activity. Experimental results denote the effectiveness of the proposed approach, since it outperforms other ELM-based classification schemes in all the cases.
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
Analysis of the enzyme network involved in cattle milk production using graph theory.
Ghorbani, Sholeh; Tahmoorespur, Mojtaba; Masoudi Nejad, Ali; Nasiri, Mohammad; Asgari, Yazdan
2015-06-01
Understanding cattle metabolism and its relationship with milk products is important in bovine breeding. A systemic view could lead to consequences that will result in a better understanding of existing concepts. Topological indices and quantitative characterizations mostly result from the application of graph theory on biological data. In the present work, the enzyme network involved in cattle milk production was reconstructed and analyzed based on available bovine genome information using several public datasets (NCBI, Uniprot, KEGG, and Brenda). The reconstructed network consisted of 3605 reactions named by KEGG compound numbers and 646 enzymes that catalyzed the corresponding reactions. The characteristics of the directed and undirected network were analyzed using Graph Theory. The mean path length was calculated to be4.39 and 5.41 for directed and undirected networks, respectively. The top 11 hub enzymes whose abnormality could harm bovine health and reduce milk production were determined. Therefore, the aim of constructing the enzyme centric network was twofold; first to find out whether such network followed the same properties of other biological networks, and second, to find the key enzymes. The results of the present study can improve our understanding of milk production in cattle. Also, analysis of the enzyme network can help improve the modeling and simulation of biological systems and help design desired phenotypes to increase milk production quality or quantity.
b-tree facets for the simple graph partitioning polytope
DEFF Research Database (Denmark)
Sørensen, Michael Malmros
2004-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each consisting of no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we introduce a large class of facet defining inequalities...... for the simple graph partitioning polytopes P_n(b), b >= 3, associated with the complete graph on n nodes. These inequalities are induced by a graph configuration which is built upon trees of cardinality b. We provide a closed-form theorem that states all necessary and sufficient conditions for the facet...
b-Tree Facets for the Simple Graph Partitioning Polytope
DEFF Research Database (Denmark)
Sørensen, Michael Malmros
2000-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each consisting of no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we introduce a large class of facet defining inequalities...... for the simple graph partitioning polytopes P_n(b), b >= 3, associated with the complete graph on n nodes. These inequalities are induced by a graph configuration which is built upon trees of cardinality b. We provide a closed-form theorem that states all necessary and sufficient conditions for the facet...
Graphs of groups on surfaces interactions and models
White, AT
2001-01-01
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
Bipartite graph partitioning and data clustering
Energy Technology Data Exchange (ETDEWEB)
Zha, Hongyuan; He, Xiaofeng; Ding, Chris; Gu, Ming; Simon, Horst D.
2001-05-07
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, the authors propose a new data clustering method based on partitioning the underlying biopartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. They show that an approximate solution to the minimization problem can be obtained by computing a partial singular value decomposition (SVD) of the associated edge weight matrix of the bipartite graph. They point out the connection of their clustering algorithm to correspondence analysis used in multivariate analysis. They also briefly discuss the issue of assigning data objects to multiple clusters. In the experimental results, they apply their clustering algorithm to the problem of document clustering to illustrate its effectiveness and efficiency.
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
Spanners for geometric intersection graphs with applications
Directory of Open Access Journals (Sweden)
Martin Fürer
2012-05-01
Full Text Available A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t times the distance between u and v inG. In this paper, we consider the problem of efficiently constructing sparse spanners of ball graphs which supports fast shortest path distance queries.We present the first algorithm for constructing spanners of ball graphs. For a ball graph in Rk, we construct a (1+ε-spanner for any ε>0 with O(nε-k+1 edges in O(n2ℓ+δε-k logℓ S time, using an efficient partitioning of space into hypercubes and solving intersection problems. Here ℓ=1-1/(⌊k/2⌋+2, δ is any positive constant, and S is the ratio between the largest and smallest radius. For the special case when the balls all have unit size, we show that the complexity of constructing a (1+ε-spanner is almost equal to the complexity of constructing a Euclidean minimum spanning tree. The algorithm extends naturally to other disk-likeobjects, also in higher dimensions.The algorithm uses an efficient subdivision of space to construct a sparse graph having many of the same distance properties as the input ball graph. Additionally, the constructed spanners have a small vertex separator decomposition (hereditary. In dimension k=2, the disk graph spanner has an O(n1/2ε-3/2+ε-3log S separator. The presence of a small separator is then exploited to obtain very efficient data structures for approximate distance queries. The results on geometric graph separators might be of independent interest. For example, since complete Euclidean graphs are just a special case of (unit ball graphs, our results also provide a new approach for constructing spanners with small separators in these 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.
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
DEFF Research Database (Denmark)
Thomassen, Carsten
2014-01-01
We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k.......We prove a general result on graph factors modulo k . A special case says that, for each natural number k , every (12k−7)-edge-connected graph with an even number of vertices contains a spanning subgraph in which each vertex has degree congruent to k modulo 2k....
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
Directory of Open Access Journals (Sweden)
Borowiecka-Olszewska Marta
2017-05-01
Full Text Available A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced subgraphs are consecutively colourable, too. We call elements of this class perfect consecutively colourable to emphasise the conceptual similarity to perfect graphs. Obviously, the class of perfect consecutively colourable graphs is induced hereditary, so it can be characterized by the family of induced forbidden graphs. In this work we give a necessary and sufficient conditions that must be satisfied by the generalized Sevastjanov rosette to be an induced forbid- den graph for the class of perfect consecutively colourable graphs. Along the way, we show the exact values of the deficiency of all generalized Sevastjanov rosettes, which improves the earlier known estimating result. It should be mentioned that the deficiency of a graph measures its closeness to the class of consecutively colourable graphs. We motivate the investigation of graphs considered here by showing their connection to the class of planar perfect consecutively colourable graphs.
SING: subgraph search in non-homogeneous graphs.
Di Natale, Raffaele; Ferro, Alfredo; Giugno, Rosalba; Mongiovì, Misael; Pulvirenti, Alfredo; Shasha, Dennis
2010-02-19
Finding the subgraphs of a graph database that are isomorphic to a given query graph has practical applications in several fields, from cheminformatics to image understanding. Since subgraph isomorphism is a computationally hard problem, indexing techniques have been intensively exploited to speed up the process. Such systems filter out those graphs which cannot contain the query, and apply a subgraph isomorphism algorithm to each residual candidate graph. The applicability of such systems is limited to databases of small graphs, because their filtering power degrades on large graphs. In this paper, SING (Subgraph search In Non-homogeneous Graphs), a novel indexing system able to cope with large graphs, is presented. The method uses the notion of feature, which can be a small subgraph, subtree or path. Each graph in the database is annotated with the set of all its features. The key point is to make use of feature locality information. This idea is used to both improve the filtering performance and speed up the subgraph isomorphism task. Extensive tests on chemical compounds, biological networks and synthetic graphs show that the proposed system outperforms the most popular systems in query time over databases of medium and large graphs. Other specific tests show that the proposed system is effective for single large graphs.
Characterisations of Intersection Graphs by Vertex Orderings
Wood, David R.
2004-01-01
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs, co-comparability graphs, AT-free graphs, and split graphs have bandwidth bounded by their maximum degree.
Dafik; Hesti Agustin, Ika; Nurvitaningrum, A. I.; Prihandini, R. M.
2017-06-01
All graphs in this paper are simple, finite, and undirected graph. Let r be a edges of H. The edge comb product between L and H, denoted by L⊵H, is a graph obtained by taking one copy of L and |E(L)| copies of H and grafting the i-th copy of H at the edges r to the i-th edges of L, we call such a graph as an edge comb product of graph with subgraph as a terminal of its amalgamation, denoted by G = K⊵Amal(H, L ⊂ H, n). The graph G is said to admits an (a, d)-H-antimagic total labeling if there exist a bijection f : V(G) ∪ E(G) → {1, 2, …, |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W (H) = ∑ v∈V(H) f(v) + ∑e∈E(H) f(e) form an arithmetic sequence {a, a + d, a + 2d, …, a + (t - 1)d}, where a and d are positive integers and t is the number of all subgraphs isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study the super H-antimagicness of disjoint union of edge comb product of graphs with subgraph as a terminal of its amalgamation.
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.
Directory of Open Access Journals (Sweden)
Karolina Taczanowska
2017-12-01
Full Text Available Mountain protected areas (PAs aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers collected in Tatra National Park (TNP, Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph. In a second step, the actual use of the area by skiers (functional network; directed graph was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: β, γ, α, movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure.
A conjugate gradient method for the spectral partitioning of graphs
Kruyt, Nicolaas P.
1997-01-01
The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and
Directory of Open Access Journals (Sweden)
A. Assari
2016-01-01
Full Text Available In this paper, a graph is assigned to any probability measure on the σ-algebra of Borel sets of a topological space. Using this construction, it is proved that given any number n (finite or infinite there exists a nonregular graph such that its clique, chromatic, and dominating number equals n.
De Jong, Marvin L.
1993-01-01
Describes the powerful graphing ability of computer algebra systems (CAS) to create three-dimensional graphs or surface graphics of electric potentials. Provides equations along with examples of the printouts. Lists the programs Mathematica, Maple, Derive, Theorist, MathCad, and MATLAB as promising CAS systems. (MVL)
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
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
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...
Moment graphs and representations
DEFF Research Database (Denmark)
Jantzen, Jens Carsten
2012-01-01
Moment graphs and sheaves on moment graphs are basically combinatorial objects that have be used to describe equivariant intersectiion cohomology. In these lectures we are going to show that they can be used to provide a direct link from this cohomology to the representation theory of simple Lie...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
Parity, cycle space, and K4-subdivisions in graphs
DEFF Research Database (Denmark)
Thomassen, Carsten
1999-01-01
We survey some parity arguments and problems in graph theory, in particular some that can be attacked using the cycle space of a graph. We discuss some results on specific collections of cyclesthat generate the cycle space. We explain how thespace generated by the cycles through two prescribed...... edges in a graph is used in a proof of the conjecturemade by B. Toft in 1974 that every $4$-chromatic graph contains atotally odd $K_4$-subdivision, that is, a subdivision of $K_4$ in which each edge of $K_4$ corresponds to an odd path. (Another proof of Toft's conjecture was found independently by W....... Zang). We prove the new result that every $4$-connected graph with at least three triangles contains a totally odd $K_4$-subdivision if and only if it does notcontain a vertex whose deletion results in a bipartite graph.In particular, every $4$-connected planar graph contains a totally odd $K_4...
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...
Product of Locally Primitive Graphs
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Amir Assari
2014-01-01
Full Text Available Many large graphs can be constructed from existing smaller graphs by using graph operations, such as the product of two graphs. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this paper we consider the product of two locally primitive graphs and prove that only tensor product of them will also be locally primitive.
Directory of Open Access Journals (Sweden)
Nicole Geberzahn
Full Text Available BACKGROUND: Birdsong is a popular model system in research areas such as vocal communication, neuroethology or neuroendocrinology of behaviour. As most research has been conducted on species with male-only song production, the hormone-dependency of male song is well established. However, female singing and its mechanisms are poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: We characterised the song and its endocrine correlates of blue-capped cordon-bleus (Uraeginthus cyanocephalus, a species in which both sexes sing. Like other estrildids, they produce directed song during courtship and undirected (or solitary song in isolation, i.e. when the mate is not visible or absent. We compare solitary song of blue-capped cordon-bleus to published descriptions of the song of its relative, the zebra finch (Taeniopygia guttata. Solitary song of cordon-bleus shared some overall song features with that of zebra finches but differed in spectro-temporal song features, sequential stereotypy and sequential organisation. The song of cordon-bleus was dimorphic with respect to the larger size of syllable repertoires, the higher song duration and the lower variability of pitch goodness (measuring the pureness of harmonic sounds in males. However, in both sexes the overall plasma testosterone concentrations were low (ca. 300 pg/ml and did not correlate with the sexually dimorphic song motor pattern. Despite such low concentrations, the increase in the rate of solitary song coincided with an increase in the level of testosterone. Furthermore, the latency to start singing after the separation from the mate was related to hormone levels. CONCLUSIONS/SIGNIFICANCE: Our findings suggest that the occurrence of solitary song but not its motor pattern might be under the control of testosterone in female and male cordon-bleus.
Graph Abstraction and Abstract Graph Transformation
Boneva, I.B.; Rensink, Arend; Kurban, M.E.; Bauer, J.
2007-01-01
Many important systems like concurrent heap-manipulating programs, communication networks, or distributed algorithms are hard to verify due to their inherent dynamics and unboundedness. Graphs are an intuitive representation of states of these systems, where transitions can be conveniently described
Graph Edge Coloring Vizing's Theorem and Goldberg's Conjecture
Stiebitz, Michael; Toft, Bjarne; Favrholdt, Lene M
2012-01-01
Features recent advances and new applications in graph edge coloring Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring. The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explor
Exploring community structure in biological networks with random graphs
2014-01-01
Background Community structure is ubiquitous in biological networks. There has been an increased interest in unraveling the community structure of biological systems as it may provide important insights into a system’s functional components and the impact of local structures on dynamics at a global scale. Choosing an appropriate community detection algorithm to identify the community structure in an empirical network can be difficult, however, as the many algorithms available are based on a variety of cost functions and are difficult to validate. Even when community structure is identified in an empirical system, disentangling the effect of community structure from other network properties such as clustering coefficient and assortativity can be a challenge. Results Here, we develop a generative model to produce undirected, simple, connected graphs with a specified degrees and pattern of communities, while maintaining a graph structure that is as random as possible. Additionally, we demonstrate two important applications of our model: (a) to generate networks that can be used to benchmark existing and new algorithms for detecting communities in biological networks; and (b) to generate null models to serve as random controls when investigating the impact of complex network features beyond the byproduct of degree and modularity in empirical biological networks. Conclusion Our model allows for the systematic study of the presence of community structure and its impact on network function and dynamics. This process is a crucial step in unraveling the functional consequences of the structural properties of biological systems and uncovering the mechanisms that drive these systems. PMID:24965130
Density conditions for triangles in multipartite graphs
DEFF Research Database (Denmark)
Bondy, Adrian; Shen, Jin; Thomassé, Stephan
2006-01-01
subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has......We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erdos, we prove that, if the minimum degree of G is at least 9 vertical bar V(G)vertical bar/10, the largest triangle-free subgraphs are precisely the largest bipartite...... a triangle, provided that the edge density between any two parts is greater than 1/2....
Spanners for geometric intersection graphs with applications
Martin Fürer; Shiva Prasad Kasiviswanathan
2012-01-01
A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real numbert>1, we say that a subgraph G' of a graph G is a t-spanner of G, if for every pair of verticesu,v in G, there exists a path in G' of length at most t times the distance between u and v inG. In this paper, we consider the problem of efficiently constructing sparse spanners of ball graphs which supports fast shortest path distance queries.We present the first algorithm for constructing spanners o...
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.
Modification of Prim’s algorithm on complete broadcasting graph
Dairina; Arif, Salmawaty; Munzir, Said; Halfiani, Vera; Ramli, Marwan
2017-09-01
Broadcasting is an information dissemination from one object to another object through communication between two objects in a network. Broadcasting for n objects can be solved by n - 1 communications and minimum time unit defined by ⌈2log n⌉ In this paper, weighted graph broadcasting is considered. The minimum weight of a complete broadcasting graph will be determined. Broadcasting graph is said to be complete if every vertex is connected. Thus to determine the minimum weight of complete broadcasting graph is equivalent to determine the minimum spanning tree of a complete graph. The Kruskal’s and Prim’s algorithm will be used to determine the minimum weight of a complete broadcasting graph regardless the minimum time unit ⌈2log n⌉ and modified Prim’s algorithm for the problems of the minimum time unit ⌈2log n⌉ is done. As an example case, here, the training of trainer problem is solved using these algorithms.
Non-heuristic reduction of the graph in graph-cut optimization
International Nuclear Information System (INIS)
Malgouyres, François; Lermé, Nicolas
2012-01-01
During the last ten years, graph cuts had a growing impact in shape optimization. In particular, they are commonly used in applications of shape optimization such as image processing, computer vision and computer graphics. Their success is due to their ability to efficiently solve (apparently) difficult shape optimization problems which typically involve the perimeter of the shape. Nevertheless, solving problems with a large number of variables remains computationally expensive and requires a high memory usage since underlying graphs sometimes involve billion of nodes and even more edges. Several strategies have been proposed in the literature to improve graph-cuts in this regards. In this paper, we give a formal statement which expresses that a simple and local test performed on every node before its construction permits to avoid the construction of useless nodes for the graphs typically encountered in image processing and vision. A useless node is such that the value of the maximum flow in the graph does not change when removing the node from the graph. Such a test therefore permits to limit the construction of the graph to a band of useful nodes surrounding the final cut.
DEFF Research Database (Denmark)
Gutin, Gregory; Kim, Eun Jung; Soleimanfallah, Arezou
2012-01-01
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if the given graph is bipartite with partition U V, and each ...
Total Flooding Time and Rumor Propagation on Graphs
Camargo, Darcy; Popov, Serguei
2017-03-01
We study the discrete time version of the flooding time problem as a model of rumor propagation where each site in the graph has initially a distinct piece of information; we are interested in the number of "conversations" before the entire graph knows all pieces of information. For the complete graph we compare the ratio between the expected propagation time for all pieces of information and the corresponding time for a single piece of information, obtaining the asymptotic ratio 3 / 2 between them.
Learning Probabilistic Decision Graphs
DEFF Research Database (Denmark)
Jaeger, Manfred; Dalgaard, Jens; Silander, Tomi
2004-01-01
Probabilistic decision graphs (PDGs) are a representation language for probability distributions based on binary decision diagrams. PDGs can encode (context-specific) independence relations that cannot be captured in a Bayesian network structure, and can sometimes provide computationally more...
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.
Efficiently Controllable Graphs.
Gokler, Can; Lloyd, Seth; Shor, Peter; Thompson, Kevin
2017-06-30
We investigate graphs that can be disconnected into small components by removing a vanishingly small fraction of their vertices. We show that, when a controllable quantum network is described by such a graph and the gaps in eigenfrequencies and in transition frequencies are bounded exponentially in the number of vertices, the network is efficiently controllable, in the sense that universal quantum computation can be performed using a control sequence polynomial in the size of the network while controlling a vanishingly small fraction of subsystems. We show that networks corresponding to finite-dimensional lattices are efficiently controllable and explore generalizations to percolation clusters and random graphs. We show that the classical computational complexity of estimating the ground state of Hamiltonians described by controllable graphs is polynomial in the number of subsystems or qubits.
Interaction Graphs: Exponentials
Seiller, Thomas
2013-01-01
This paper is the fourth of a series exposing a systematic combinatorial approach to Girard's Geometry of Interaction program. This program aims at obtaining particular realizability models for linear logic that accounts for the dynamics of cut-elimination. This fourth paper tackles the complex issue of defining exponential connectives in this framework. In order to succeed in this, we use the notion of graphings, a generalization of graphs which was defined in earlier work. We explain how we...
DEFF Research Database (Denmark)
Bakhshesh, Davood; Barba, Luis; Bose, Prosenjit
2018-01-01
In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points S⊂R2 and an angle 0Yao graph cY(θ) with vertex set S and angle θ as follows. For each p,q∈S, we add an edge from p to q in cY(θ) if there exists a cone with apex p...
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.
Local Interaction on Random Graphs
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Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
Rashmanlou, Hossein; Samanta, Sovan; Pal, Madhumangal; Borzooei, R A
2016-01-01
The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.
Commuting projections on graphs
Energy Technology Data Exchange (ETDEWEB)
Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2013-02-19
For a given (connected) graph, we consider vector spaces of (discrete) functions defined on its vertices and its edges. These two spaces are related by a discrete gradient operator, Grad and its adjoint, ₋Div, referred to as (negative) discrete divergence. We also consider a coarse graph obtained by aggregation of vertices of the original one. Then a coarse vertex space is identified with the subspace of piecewise constant functions over the aggregates. We consider the ℓ_{2}-projection Q_{H} onto the space of these piecewise constants. In the present paper, our main result is the construction of a projection π _{H} from the original edge-space onto a properly constructed coarse edge-space associated with the edges of the coarse graph. The projections π _{H} and Q_{H} commute with the discrete divergence operator, i.e., we have div π _{H} = Q_{H} div. The respective pair of coarse edge-space and coarse vertexspace offer the potential to construct two-level, and by recursion, multilevel methods for the mixed formulation of the graph Laplacian which utilizes the discrete divergence operator. The performance of one two-level method with overlapping Schwarz smoothing and correction based on the constructed coarse spaces for solving such mixed graph Laplacian systems is illustrated on a number of graph examples.
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 ...
PERANCANGAN SISTEM PENJADWALAN PEMBELAJARAN MENGGUNAKAN GRAPH COLORING
Directory of Open Access Journals (Sweden)
Taufik Hidayatulloh
2016-03-01
Full Text Available Abstract - In learning scheduling problem often faced by schools in the new academic year. Sometimes collisions on the schedule was not found when the learning process has begun, so it is necessary to re-schedule on the schedule. And this resulted in the teaching and learning first weeks less to run well. Researchers previously have used various methods to solve the scheduling as Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (coloring of a graph is the simplest method and the experimental results indicate that the development of methods of scheduling Graph Coloring deliver results that meet an average of 93% across the specified constraints. At the time of split schedules that require extra energy at the start of learning did not experience a collision. With this system is expected to facilitate the allocation of space, teachers, lessons to avoid a collision. Keywords: Information Systems, Scheduling, graph coloring Abstraksi - Dalam masalah penjadwalan pembelajaran sering dihadapi sekolah pada tahun ajaran baru. Terkadang tabrakan pada jadwal itu baru ditemukan ketika proses belajar mengajar telah dimulai, sehingga perlu dilakukan penjadwalan ulang pada jadwal tersebut. Dan hal ini mengakibatkan kegiatan belajar mengajar pada minggu-minggu pertama kurang dapat berjalan dengan baik. Para peneliti sebelumnya telah menggunakan berbagai metode untuk memecahkan penjadwalan seperti Tabu search, Simulated Annealing, Network Flow, Graph Coloring. Graph Coloring (pewarnaan graf merupakan metode yang paling sederhana dan hasil percobaan menunjukkan bahwa pengembangan metode Graph Coloring memberikan hasil penjadwalan yang memenuhi rata-rata 93% seluruh constraints yang ditentukan. Pada saat membagi jadwal memerlukan energi ekstra agar pada saat di mulai pembelajaran tidak mengalami tabrakan. Dengan sistem ini diharapkan dapat mempermudah dalam mengalokasikan ruangan, guru, pelajaran agar tidak mengalami tabrakan. Kata
Hierarchy of graph matchbox manifolds
Lukina, Olga
2011-01-01
We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusi...
Linear representation of a graph
Directory of Open Access Journals (Sweden)
Eduardo Montenegro
2019-10-01
Full Text Available In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\\mathbb{R}$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area
Co-clustering directed graphs to discover asymmetries and directional communities.
Rohe, Karl; Qin, Tai; Yu, Bin
2016-10-21
In directed graphs, relationships are asymmetric and these asymmetries contain essential structural information about the graph. Directed relationships lead to a new type of clustering that is not feasible in undirected graphs. We propose a spectral co-clustering algorithm called di-sim for asymmetry discovery and directional clustering. A Stochastic co-Blockmodel is introduced to show favorable properties of di-sim To account for the sparse and highly heterogeneous nature of directed networks, di-sim uses the regularized graph Laplacian and projects the rows of the eigenvector matrix onto the sphere. A nodewise asymmetry score and di-sim are used to analyze the clustering asymmetries in the networks of Enron emails, political blogs, and the Caenorhabditis elegans chemical connectome. In each example, a subset of nodes have clustering asymmetries; these nodes send edges to one cluster, but receive edges from another cluster. Such nodes yield insightful information (e.g., communication bottlenecks) about directed networks, but are missed if the analysis ignores edge direction.
On zero divisor graph of unique product monoid rings over Noetherian reversible ring
Directory of Open Access Journals (Sweden)
Ebrahim Hashemi
2016-02-01
Full Text Available Let $R$ be an associative ring with identity and $Z^*(R$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $Gamma(R$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring over reversible right (or left Noetherian ring $R$. We essentially classify the diameter-structure of this graph and show that $0leq mbox{diam}(Gamma(Rleq mbox{diam}(Gamma(R[M]leq 3$. Moreover, we give a characterization for the possible diam$(Gamma(R$ and diam$(Gamma(R[M]$, when $R$ is a reversible Noetherian ring and $M$ is a u.p.-monoid. Also, we study relations between the girth of $Gamma(R$ and that of $Gamma(R[M]$.
Some isomorphic properties ofm-polar fuzzy graphs with applications.
Ghorai, Ganesh; Pal, Madhumangal
2016-01-01
The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m -polar fuzzy information by combining the theory of m -polar fuzzy sets with graphs. We introduce the notion of weak self complement m -polar fuzzy graphs and establish a necessary condition for m -polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement m -polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an m -polar fuzzy graphs are also defined and proved that isomorphic m -polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic m -polar fuzzy graphs. Finally, a relative study of complement and operations on m -polar fuzzy graphs have been made. Applications of m -polar fuzzy graph are also given at the end.
QAPV: a polynomial invariant for graph isomorphism testing
Directory of Open Access Journals (Sweden)
Valdir Agustinho de Melo
2013-08-01
Full Text Available To each instance of the Quadratic Assignment Problem (QAP a relaxed instance can be associated. Both variances of their solution values can be calculated in polynomial time. The graph isomorphism problem (GIP can be modeled as a QAP, associating its pair of data matrices with a pair of graphs of the same order and size. We look for invariant edge weight functions for the graphs composing the instances in order to try to find quantitative differences between variances that could be associated with the absence of isomorphism. This technique is sensitive enough to show the effect of a single edge exchange between two regular graphs of up to 3,000 vertices and 300,000 edges with degrees up to 200. Planar graph pairs from a dense family up to 300,000 vertices were also discriminated. We conjecture the existence of functions able to discriminate non-isomorphic pairs for every instance of the problem.
Facet Defining Inequalities for the Simple Graph Partioning Polytope
DEFF Research Database (Denmark)
Sørensen, Michael Malmros
2000-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each containing at most b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we investigate the facial structure of the simple graph partitio...... partitioning polytopes P(b), b = 3,...,n, associated with the complete graph on n nodes. In particular we introduce two new classes af facet defining inequalities that are induced by cliques and multistars....
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.
A first course in graph theory and combinatorics
Cioabă, Sebastian M
2009-01-01
The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.
Large-scale Graph Computation on Just a PC
2014-05-01
Squares (ALS) algorithm [157], by adapting a GraphLab implementation [96]. We used ALS to solve the Netflix movie rating prediction problem [19]: in...graph from disk, or to transfer it over a network to a cluster. 45 Graph Name Vertices Edges P Preproc. live-journal [11] 4.8M 69M 3 0.5 min netflix ...26 min [119] Webgraph-BP & yahoo- web 1 Pegasus (Hadoop) on 100 machines: 22 min 27 min [74] ALS & netflix -mm, D=20 10 GraphLab on AMD server: 4.7
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.
Facet-defining inequalities for the simple graph partitioning polytope
DEFF Research Database (Denmark)
Sørensen, Michael Malmros
2007-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually node-disjoint subgraphs, each containing at most b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we provide several classes of facet-defining inequalities...
Power domination of the cartesian product of graphs
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K.M. Koh
2016-04-01
Full Text Available In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs is a tree.
On toughness and hamiltonicity of 2K2-free graphs
Broersma, Haitze J.; Patel, Viresh; Pyatkin, Artem
The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields |A|/t components. Determining toughness is an NP-hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that
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.
Probabilistic decision graphs for optimization under uncertainty
DEFF Research Database (Denmark)
Jensen, Finn V.; Nielsen, Thomas Dyhre
2011-01-01
This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker. As the me......This paper provides a survey on probabilistic decision graphs for modeling and solving decision problems under uncertainty. We give an introduction to influence diagrams, which is a popular framework for representing and solving sequential decision problems with a single decision maker...... the development of alternative representation languages, which enlarge the class of decision problems that can be modeled efficiently. We present some of these alternative frameworks and demonstrate their expressibility using several examples. Finally, we provide a list of software systems that implement...
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.
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...
Indian Academy of Sciences (India)
The basic complexity question of the decision problem for the co-Roman domination number takes the following form: Co-Roman Domination (CRDM). Instance. A nontrivial connected graph G = (V,E) and a positive integer k. Question. Does G have a co-Roman dominating function f with w(f ) ≤ k? We proceed to prove that ...
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
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...
MISAGA: An Algorithm for Mining Interesting Subgraphs in Attributed Graphs.
He, Tiantian; Chan, Keith C C
2017-04-25
An attributed graph contains vertices that are associated with a set of attribute values. Mining clusters or communities, which are interesting subgraphs in the attributed graph is one of the most important tasks of graph analytics. Many problems can be defined as the mining of interesting subgraphs in attributed graphs. Algorithms that discover subgraphs based on predefined topologies cannot be used to tackle these problems. To discover interesting subgraphs in the attributed graph, we propose an algorithm called mining interesting subgraphs in attributed graph algorithm (MISAGA). MISAGA performs its tasks by first using a probabilistic measure to determine whether the strength of association between a pair of attribute values is strong enough to be interesting. Given the interesting pairs of attribute values, then the degree of association is computed for each pair of vertices using an information theoretic measure. Based on the edge structure and degree of association between each pair of vertices, MISAGA identifies interesting subgraphs by formulating it as a constrained optimization problem and solves it by identifying the optimal affiliation of subgraphs for the vertices in the attributed graph. MISAGA has been tested with several large-sized real graphs and is found to be potentially very useful for various applications.
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...
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
Towards information inequalities for generalized graph entropies.
Directory of Open Access Journals (Sweden)
Lavanya Sivakumar
Full Text Available In this article, we discuss the problem of establishing relations between information measures for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the Rényi entropy have been considered for this study. Our main results involve establishing formal relationships, by means of inequalities, between these two kinds of measures. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and partition-independent entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.
Unraveling protein networks with power graph analysis.
Directory of Open Access Journals (Sweden)
Loïc Royer
Full Text Available Networks play a crucial role in computational biology, yet their analysis and representation is still an open problem. Power Graph Analysis is a lossless transformation of biological networks into a compact, less redundant representation, exploiting the abundance of cliques and bicliques as elementary topological motifs. We demonstrate with five examples the advantages of Power Graph Analysis. Investigating protein-protein interaction networks, we show how the catalytic subunits of the casein kinase II complex are distinguishable from the regulatory subunits, how interaction profiles and sequence phylogeny of SH3 domains correlate, and how false positive interactions among high-throughput interactions are spotted. Additionally, we demonstrate the generality of Power Graph Analysis by applying it to two other types of networks. We show how power graphs induce a clustering of both transcription factors and target genes in bipartite transcription networks, and how the erosion of a phosphatase domain in type 22 non-receptor tyrosine phosphatases is detected. We apply Power Graph Analysis to high-throughput protein interaction networks and show that up to 85% (56% on average of the information is redundant. Experimental networks are more compressible than rewired ones of same degree distribution, indicating that experimental networks are rich in cliques and bicliques. Power Graphs are a novel representation of networks, which reduces network complexity by explicitly representing re-occurring network motifs. Power Graphs compress up to 85% of the edges in protein interaction networks and are applicable to all types of networks such as protein interactions, regulatory networks, or homology networks.
Network evolution driven by dynamics applied to graph coloring
International Nuclear Information System (INIS)
Wu Jian-She; Li Li-Guang; Yu Xin; Jiao Li-Cheng; Wang Xiao-Hua
2013-01-01
An evolutionary network driven by dynamics is studied and applied to the graph coloring problem. From an initial structure, both the topology and the coupling weights evolve according to the dynamics. On the other hand, the dynamics of the network are determined by the topology and the coupling weights, so an interesting structure-dynamics co-evolutionary scheme appears. By providing two evolutionary strategies, a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics. The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors. In this way, a co-evolution phenomenon is applied to the graph coloring problem. The proposed scheme is tested on several benchmark graphs for graph coloring
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.
A Robust PTAS for Maximum Weight Independent Sets in Unit Disk Graphs
Nieberg, T.; Hurink, Johann L.; Kern, Walter; Hromkovič, Juraj; Nagel, Manfred; Westfechtel, Bernhard
2004-01-01
A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric
A new PTAS for maximum independent sets in unit disk graphs
Nieberg, T.; Hurink, Johann L.; Kern, Walter
2003-01-01
A unit disk graph is an intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric
A sampling theory for infinite weighted graphs
Directory of Open Access Journals (Sweden)
Palle E. T. Jorgensen
2011-01-01
Full Text Available We prove two sampling theorems for infinite (countable discrete weighted graphs \\(G\\; one example being "large grids of resistors" i.e., networks and systems of resistors. We show that there is natural ambient continuum \\(X\\ containing \\(G\\, and there are Hilbert spaces of functions on \\(X\\ that allow interpolation by sampling values of the functions restricted only on the vertices in \\(G\\. We sample functions on \\(X\\ from their discrete values picked in the vertex-subset \\(G\\. We prove two theorems that allow for such realistic ambient spaces \\(X\\ for a fixed graph \\(G\\, and for interpolation kernels in function Hilbert spaces on \\(X\\, sampling only from points in the subset of vertices in \\(G\\. A continuum is often not apparent at the outset from the given graph \\(G\\. We will solve this problem with the use of ideas from stochastic integration.
Resistance Distances in Vertex-Face Graphs
Shangguan, Yingmin; Chen, Haiyan
2018-01-01
The computation of two-point resistances in networks is a classical problem in electric circuit theory and graph theory. Let G be a triangulation graph with n vertices embedded on an orientable surface. Define K(G) to be the graph obtained from G by inserting a new vertex vϕ to each face ϕ of G and adding three new edges (u, vϕ), (v, vϕ) and (w, vϕ), where u, v and w are three vertices on the boundary of ϕ. In this paper, using star-triangle transformation and resistance local-sum rules, explicit relations between resistance distances in K(G) and those in G are obtained. These relations enable us to compute resistance distance between any two points of Kk(G) recursively. As explanation examples, some resistances in several networks are computed, including the modified Apollonian network and networks constructed from tetrahedron, octahedron and icosahedron, respectively.
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 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
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Rensink, Arend
In this paper we describe our intended approach for the verification of software written in imperative programming languages. We base our approach on model checking of graph transition systems, where each state is a graph and the transitions are specified by graph transformation rules. We believe
Robustness of random graphs based on graph spectra.
Wu, Jun; Barahona, Mauricio; Tan, Yue-Jin; Deng, Hong-Zhong
2012-12-01
It has been recently proposed that the robustness of complex networks can be efficiently characterized through the natural connectivity, a spectral property of the graph which corresponds to the average Estrada index. The natural connectivity corresponds to an average eigenvalue calculated from the graph spectrum and can also be interpreted as the Helmholtz free energy of the network. In this article, we explore the use of this index to characterize the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices. We show both analytically and numerically that the natural connectivity of ER random graphs increases linearly with the average degree. It is also shown that ER random graphs are more robust than the corresponding random regular graphs with the same number of vertices and edges. However, the relative robustness of ER random graphs and regular ring lattices depends on the average degree and graph size: there is a critical graph size above which regular ring lattices are more robust than random graphs. We use our analytical results to derive this critical graph size as a function of the average degree.
Codes related to line graphs of triangular graphs and permutation ...
African Journals Online (AJOL)
For any prime p, we consider p-ary linear codes obtained from the row span of incidence matrices of line graphs of triangular graphs and adjacency matrices of their line graphs. We determine parameters of the codes, their automorphism groups and exhibit permutation decoding sets (PD-sets) for partial permutation ...
Linear Time Vertex Partitioning on Massive Graphs
Mell, Peter; Harang, Richard; Gueye, Assane
2016-01-01
The problem of optimally removing a set of vertices from a graph to minimize the size of the largest resultant component is known to be NP-complete. Prior work has provided near optimal heuristics with a high time complexity that function on up to hundreds of nodes and less optimal but faster techniques that function on up to thousands of nodes. In this work, we analyze how to perform vertex partitioning on massive graphs of tens of millions of nodes. We use a previously known and very simple heuristic technique: iteratively removing the node of largest degree and all of its edges. This approach has an apparent quadratic complexity since, upon removal of a node and adjoining set of edges, the node degree calculations must be updated prior to choosing the next node. However, we describe a linear time complexity solution using an array whose indices map to node degree and whose values are hash tables indicating the presence or absence of a node at that degree value. This approach also has a linear growth with respect to memory usage which is surprising since we lowered the time complexity from quadratic to linear. We empirically demonstrate linear scalability and linear memory usage on random graphs of up to 15000 nodes. We then demonstrate tractability on massive graphs through execution on a graph with 34 million nodes representing Internet wide router connectivity. PMID:27336059
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.
Incremental Frequent Subgraph Mining on Large Evolving Graphs
Abdelhamid, Ehab
2017-08-22
Frequent subgraph mining is a core graph operation used in many domains, such as graph data management and knowledge exploration, bioinformatics and security. Most existing techniques target static graphs. However, modern applications, such as social networks, utilize large evolving graphs. Mining these graphs using existing techniques is infeasible, due to the high computational cost. In this paper, we propose IncGM+, a fast incremental approach for continuous frequent subgraph mining problem on a single large evolving graph. We adapt the notion of “fringe” to the graph context, that is the set of subgraphs on the border between frequent and infrequent subgraphs. IncGM+ maintains fringe subgraphs and exploits them to prune the search space. To boost the efficiency, we propose an efficient index structure to maintain selected embeddings with minimal memory overhead. These embeddings are utilized to avoid redundant expensive subgraph isomorphism operations. Moreover, the proposed system supports batch updates. Using large real-world graphs, we experimentally verify that IncGM+ outperforms existing methods by up to three orders of magnitude, scales to much larger graphs and consumes less memory.
Visualizing automorphisms of graph algebras
DEFF Research Database (Denmark)
Avery, James Emil; Johansen, Rune; Szymanski, Wojciech
2018-01-01
Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduces the permutation graph for a permutative endomorphism of a graph C*-algebra as a labeled directed multigraph...... that gives a visual representation of the endomorphism and facilitates computations. Combinatorial criteria have previously been developed for deciding when such an endomorphism is an automorphism, but here the question is reformulated in terms of the permutation graph and new proofs are given. Furthermore......, it is shown how to use permutation graphs to efficiently generate exhaustive collections of permutative automorphisms. Permutation graphs provide a natural link to the textile systems representing induced endomorphisms on the edge shift of the given graph, and this allows the powerful tools of the theory...
Rensink, Arend; Schmidt, David
2004-01-01
Graphs are an intuitive model for states of a (software) system that include pointer structures | for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order
Rensink, Arend; Schmidt, D.A.
2004-01-01
Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary
Dujmović, Vida; Sidiropoulos, Anastasios; Wood, David R.
2015-01-01
Bourgain and Yehudayoff recently constructed $O(1)$-monotone bipartite expanders. By combining this result with a generalisation of the unraveling method of Kannan, we construct 3-monotone bipartite expanders, which is best possible. We then show that the same graphs admit 3-page book embeddings, 2-queue layouts, 4-track layouts, and have simple thickness 2. All these results are best possible.
S.M. Heditniemi (Sandra); R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2012-01-01
textabstractLet $G = (V,E)$ be a graph. A partition $\\pi = \\{V_1, V_2, \\ldots, V_k \\}$ of the vertices $V$ of $G$ into $k$ {\\it color classes} $V_i$, with $1 \\leq i \\leq k$, is called a {\\it quorum coloring} if for every vertex $v \\in V$, at least half of the vertices in the closed neighborhood
Cooper, Carol
1975-01-01
Teachers of an integrated elementary classroom used cookie-sharing time as a learning experience for students. Responsible for dividing varying amounts of cookies daily, the students learned to translate their experiences to graphs of differing sophistication and analyses. Further interpretation and application were done by individual students…
Grabmayer, C.A.; van Oostrom, V.
2014-01-01
We report on work in progress on `nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 9. Decoding Codes on Graphs - Low Density Parity Check Codes. A S Madhu Aditya Nori. General Article Volume 8 Issue 9 September 2003 pp 49-59. Fulltext. Click here to view fulltext PDF. Permanent link:
Energy Technology Data Exchange (ETDEWEB)
Simmons, G.J.
1985-01-01
Given a graph G and an ordering phi of the vertices, V(G), we define a parsimonious proper coloring (PPC) of V(G) under phi to be a proper coloring of V(G) in the order phi, where a new color is introduced only when a vertex cannot be properly colored in its order with any of the colors already used.
String graph construction using incremental hashing.
Ben-Bassat, Ilan; Chor, Benny
2014-12-15
New sequencing technologies generate larger amount of short reads data at decreasing cost. De novo sequence assembly is the problem of combining these reads back to the original genome sequence, without relying on a reference genome. This presents algorithmic and computational challenges, especially for long and repetitive genome sequences. Most existing approaches to the assembly problem operate in the framework of de Bruijn graphs. Yet, a number of recent works use the paradigm of string graph, using a variety of methods for storing and processing suffixes and prefixes, like suffix arrays, the Burrows-Wheeler transform or the FM index. Our work is motivated by a search for new approaches to constructing the string graph, using alternative yet simple data structures and algorithmic concepts. We introduce a novel hash-based method for constructing the string graph. We use incremental hashing, and specifically a modification of the Karp-Rabin fingerprint, and Bloom filters. Using these probabilistic methods might create false-positive and false-negative edges during the algorithm's execution, but these are all detected and corrected. The advantages of the proposed approach over existing methods are its simplicity and the incorporation of established probabilistic techniques in the context of de novo genome sequencing. Our preliminary implementation is favorably comparable with the first string graph construction of Simpson and Durbin (2010) (but not with subsequent improvements). Further research and optimizations will hopefully enable the algorithm to be incorporated, with noticeable performance improvement, in state-of-the-art string graph-based assemblers. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Generalised power graph compression reveals dominant relationship patterns in complex networks.
Ahnert, Sebastian E
2014-03-25
We introduce a framework for the discovery of dominant relationship patterns in complex networks, by compressing the networks into power graphs with overlapping power nodes. When paired with enrichment analysis of node classification terms, the most compressible sets of edges provide a highly informative sketch of the dominant relationship patterns that define the network. In addition, this procedure also gives rise to a novel, link-based definition of overlapping node communities in which nodes are defined by their relationships with sets of other nodes, rather than through connections within the community. We show that this completely general approach can be applied to undirected, directed, and bipartite networks, yielding valuable insights into the large-scale structure of real-world networks, including social networks and food webs. Our approach therefore provides a novel way in which network architecture can be studied, defined and classified.
Graph-based composite local Bregman divergences on discrete sample spaces.
Kanamori, Takafumi; Takenouchi, Takashi
2017-11-01
This paper develops a general framework of statistical inference on discrete sample spaces, on which a neighborhood system is defined by an undirected graph. The scoring rule is a measure of the goodness of fit for the model to observed samples, and we employ its localized version, local scoring rules, which does not require the normalization constant. We show that the local scoring rule is closely related to a discrepancy measure called composite local Bregman divergence. Then, we investigate the statistical consistency of local scoring rules in terms of the graphical structure of the sample space. Moreover, we propose a robust and computationally efficient estimator based on our framework. In numerical experiments, we investigate the relation between the neighborhood system and estimation accuracy. Also, we numerically evaluate the robustness of localized estimators. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
On dominator colorings in graphs
Indian Academy of Sciences (India)
Graph coloring and domination are two major areas in graph theory that have been ... independent set if no two vertices in S are adjacent. ... independent set. The corona G1 ◦ G2 of two graphs G1 and G2 is defined to be the graph. G obtained by taking one copy of G1 and |V(G1)| copies of G2, and then joining the i-th.
Hamiltonian paths on Platonic graphs
Directory of Open Access Journals (Sweden)
Brian Hopkins
2004-07-01
Full Text Available We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.
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.
Improving Attack Graph Visualization through Data Reduction and Attack Grouping
Energy Technology Data Exchange (ETDEWEB)
John Homer; Ashok Varikuti; Xinming Ou; Miles A. McQueen
2008-09-01
Various tools exist to analyze enterprise network systems and to produce attack graphs detailing how attackers might penetrate into the system. These attack graphs, however, are often complex and difficult to comprehend fully, and a human user may find it problematic to reach appropriate configuration decisions. This paper presents methodologies that can 1) automatically identify portions of an attack graph that do not help a user to understand the core security problems and so can be trimmed, and 2) automatically group similar attack steps as virtual nodes in a model of the network topology, to immediately increase the understandability of the data. We believe both methods are important steps toward improving visualization of attack graphs to make them more useful in configuration management for large enterprise networks. We implemented our methods using one of the existing attack-graph toolkits. Initial experimentation shows that the proposed approaches can 1) significantly reduce the complexity of attack graphs by trimming a large portion of the graph that is not needed for a user to understand the security problem, and 2) significantly increase the accessibility and understandability of the data presented in the attack graph by clearly showing, within a generated visualization of the network topology, the number and type of potential attacks to which each host is exposed.
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander)
2017-01-01
textabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G=(V,E), we define a "good" G-matrix as a V×V matrix with negative entries corresponding to adjacent nodes, zero
Nullspace embeddings for outerplanar graphs
L. Lovász (László); A. Schrijver (Alexander); M. Loebl (Martin); J. Nešetřil (Jaroslav); R. Thomas (Robin)
2017-01-01
htmlabstractWe study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a "good” G-matrix as a V × V matrix with negative
Nullspace embeddings for outerplanar graphs
Lovász, L.; Schrijver, A.; Loebl, M.; Nešetřil, J.; Thomas, R.
2017-01-01
We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph G = (V, E), we define a “good” G-matrix as a V × V matrix with negative entries corresponding to adjacent nodes, zero entries
Pattern-Based Graph Abstraction
Rensink, Arend; Zambon, Eduardo; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a new abstraction technique for the exploration of graph transformation systems with infinite state spaces. This technique is based on patterns, simple graphs describing structures of interest that should be preserved by the abstraction. Patterns are collected into pattern graphs, layered
Generalised compositionality in graph transformation
Ghamarian, A.H.; Rensink, Arend; Ehrig, H; Engels, G.; Kreowski, H.J.; Rozenberg, G.
We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph
Hopkins, Brian
2004-01-01
The interconnected world of actors and movies is a familiar, rich example for graph theory. This paper gives the history of the "Kevin Bacon Game" and makes extensive use of a Web site to analyze the underlying graph. The main content is the classroom development of the weighted average to determine the best choice of "center" for the graph. The…
Mining and Indexing Graph Databases
Yuan, Dayu
2013-01-01
Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…
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
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
We establish an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low ...
Predecessor and permutation existence problems for sequential dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Barrett, C. L. (Christopher L.); Hunt, H. B. (Harry B.); Marathe, M. V. (Madhav V.); Rosenkrantz, D. J. (Daniel J.); Stearns, R. E. (Richard E.)
2002-01-01
A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in BMR99, BR991 as a formal model for analyzing simulation systems. An SDS S is a triple (G, F,n ),w here (i) G(V,E ) is an undirected graph with n nodes with each node having a state, (ii) F = (fi, fi, . . ., fn), with fi denoting a function associated with node ui E V and (iii) A is a permutation of (or total order on) the nodes in V, A configuration of an SDS is an n-vector ( b l, bz, . . ., bn), where bi is the value of the state of node vi. A single SDS transition from one configuration to another is obtained by updating the states of the nodes by evaluating the function associated with each of them in the order given by n. Here, we address the complexity of two basic problems and their generalizations for SDSs. Given an SDS S and a configuration C, the PREDECESSOR EXISTENCE (or PRE) problem is to determine whether there is a configuration C' such that S has a transition from C' to C. (If C has no predecessor, C is known as a garden of Eden configuration.) Our results provide separations between efficiently solvable and computationally intractable instances of the PRE problem. For example, we show that the PRE problem can be solved efficiently for SDSs with Boolean state values when the node functions are symmetric and the underlying graph is of bounded treewidth. In contrast, we show that allowing just one non-symmetric node function renders the problem NP-complete even when the underlying graph is a tree (which has a treewidth of 1). We also show that the PRE problem is efficiently solvable for SDSs whose state values are from a field and whose node functions are linear. Some of the polynomial algorithms also extend to the case where we want to find an ancestor configuration that precedes a given configuration by a logarithmic number of steps. Our results extend some of the earlier results by Sutner [Su95] and Green [@87] on the complexity of
Lower and upper competitive bounds for online directed graph exploration
Foerster, Klaus-Tycho; Wattenhofer, Roger
2015-01-01
We study the problem of exploring all nodes of an unknown directed graph. A searcher has to construct a tour that visits all nodes, but only has information about the parts of the graph it already visited. Analogously to the travelling salesman problem, the goal is to minimize the cost of such a tour. In this article, we present upper and lower bounds for the competitive ratio of both the deterministic and the randomized online version of exploring all nodes of directed grap...
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.
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
Domination criticality in product graphs
Directory of Open Access Journals (Sweden)
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Dynamic Representations of Sparse Graphs
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
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.
Directory of Open Access Journals (Sweden)
Dániel Bánky
Full Text Available Biological network data, such as metabolic-, signaling- or physical interaction graphs of proteins are increasingly available in public repositories for important species. Tools for the quantitative analysis of these networks are being developed today. Protein network-based drug target identification methods usually return protein hubs with large degrees in the networks as potentially important targets. Some known, important protein targets, however, are not hubs at all, and perturbing protein hubs in these networks may have several unwanted physiological effects, due to their interaction with numerous partners. Here, we show a novel method applicable in networks with directed edges (such as metabolic networks that compensates for the low degree (non-hub vertices in the network, and identifies important nodes, regardless of their hub properties. Our method computes the PageRank for the nodes of the network, and divides the PageRank by the in-degree (i.e., the number of incoming edges of the node. This quotient is the same in all nodes in an undirected graph (even for large- and low-degree nodes, that is, for hubs and non-hubs as well, but may differ significantly from node to node in directed graphs. We suggest to assign importance to non-hub nodes with large PageRank/in-degree quotient. Consequently, our method gives high scores to nodes with large PageRank, relative to their degrees: therefore non-hub important nodes can easily be identified in large networks. We demonstrate that these relatively high PageRank scores have biological relevance: the method correctly finds numerous already validated drug targets in distinct organisms (Mycobacterium tuberculosis, Plasmodium falciparum and MRSA Staphylococcus aureus, and consequently, it may suggest new possible protein targets as well. Additionally, our scoring method was not chosen arbitrarily: its value for all nodes of all undirected graphs is constant; therefore its high value captures
Bánky, Dániel; Iván, Gábor; Grolmusz, Vince
2013-01-01
Biological network data, such as metabolic-, signaling- or physical interaction graphs of proteins are increasingly available in public repositories for important species. Tools for the quantitative analysis of these networks are being developed today. Protein network-based drug target identification methods usually return protein hubs with large degrees in the networks as potentially important targets. Some known, important protein targets, however, are not hubs at all, and perturbing protein hubs in these networks may have several unwanted physiological effects, due to their interaction with numerous partners. Here, we show a novel method applicable in networks with directed edges (such as metabolic networks) that compensates for the low degree (non-hub) vertices in the network, and identifies important nodes, regardless of their hub properties. Our method computes the PageRank for the nodes of the network, and divides the PageRank by the in-degree (i.e., the number of incoming edges) of the node. This quotient is the same in all nodes in an undirected graph (even for large- and low-degree nodes, that is, for hubs and non-hubs as well), but may differ significantly from node to node in directed graphs. We suggest to assign importance to non-hub nodes with large PageRank/in-degree quotient. Consequently, our method gives high scores to nodes with large PageRank, relative to their degrees: therefore non-hub important nodes can easily be identified in large networks. We demonstrate that these relatively high PageRank scores have biological relevance: the method correctly finds numerous already validated drug targets in distinct organisms (Mycobacterium tuberculosis, Plasmodium falciparum and MRSA Staphylococcus aureus), and consequently, it may suggest new possible protein targets as well. Additionally, our scoring method was not chosen arbitrarily: its value for all nodes of all undirected graphs is constant; therefore its high value captures importance in the
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.
Pre-service teachers challenges while interpreting statistical graphs
Wahid, Norabiatul Adawiah Abd; Rahim, Suzieleez Syrene Abdul; Zamri, Sharifah Norul Akmar Syed
2017-05-01
Nowadays statistical graphs has been widely used as a medium to communicate. Awareness of the important of statistical graphs have been realized by Ministry of Education. Therefore, Ministry of Education have included this topic into national standard curriculum as early as Standard 3. It proved that this field of study is important to our students. However pre-service teachers still faced some difficulties to comprehend various types of statistical graphs. Among the problem faced by those pre-service teachers are the difficulties to relate two statistical graphs that carrying related issues. Therefore this study will look at the types of difficulties faced by pre-service teachers when they need to interpret two statistical graphs which carried related issues. We focus on data which came from interviews which gives evidence of several problems faced by pre-service teachers when they try to comprehend those graphs that are related with each other. The discussion of results might contribute to an understanding of the complexity of the interpretation of such graphs, and to the possible solutions that can be used to cater on the problems arise.
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 of Bipolar Fuzzy Sets in Graph Structures
Directory of Open Access Journals (Sweden)
Muhammad Akram
2016-01-01
Full Text Available A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS, strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.
Directory of Open Access Journals (Sweden)
Burhan Selçuk
2017-06-01
Full Text Available Hypercube is a popular interconnection network. Due to the popularity of hypercube, more researchers pay a great effort to develop the different variants of hypercube. In this paper, we have proposed a variant of hypercube which is called as “Connected Cubic Network Graphs”, and have investigated the Hamilton-like properties of Connected Cubic Network Graphs (CCNG. Firstly, we defined CCNG and showed the characteristic analyses of CCNG. Then, we showed that the CCNG has the properties of Hamilton graph, and can be labeled using a Gray coding based recursive algorithm. Finally, we gave the comparison results, a routing algorithm and a bitonic sort algorithm for CCNG. In case of sparsity and cost, CCNG is better than Hypercube.
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.
Directory of Open Access Journals (Sweden)
Sergio Marrero-Osorio
2011-05-01
Full Text Available El autor realiza una concisa revisión sobre la aplicación de grafos en la resolución de problemas decómputo en ingeniería, enfatizando en un método propuesto por Martínez Escanaverino que utilizagrafos dicromáticos y ha sido usado en el ámbito científico técnico de Cuba. Analiza, basado en seisejemplos, el escaso empleo que se ha dado hasta el momento al software disponible para trazar yeditar los sucesivos grafos durante el proceso de resolución; estudiando y evaluando un grupo de 18editores de grafos por sus aptitudes para aplicar el mencionado método. Finalmente se recomiendauno de ellos para su uso futuro y se confirma la conveniencia de su empleo a través de unacomparación.Palabras claves: análisis estructural, resolución de problemas, algoritmos, modelo matemático, grafosdicromáticos, editores de grafos.___________________________________________________________________AbstractAuthor makes a concise review about employment of graphs in solving engineering computationalproblems, emphasizing in one method proposed by Martinez Escanaverino which uses dichromaticgraphs and has been applied in Cuban technical sciences. Analyzes, based in six examples, lack inuse (until this moment of software for graph drawing and edition through problem solving process,studying and evaluating 18 available graph editors and suggesting one of them for future applicationsof mentioned method. Finally, making a comparison, are confirmed advantages of its usage.Key words: structural analysis, problem solving, algorithms, mathematical models, dichromatic graphs,graph editors.
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Directory of Open Access Journals (Sweden)
Falcon Seth
2007-09-01
Full Text Available Abstract Graph theoretical concepts are useful for the description and analysis of interactions and relationships in biological systems. We give a brief introduction into some of the concepts and their areas of application in molecular biology. We discuss software that is available through the Bioconductor project and present a simple example application to the integration of a protein-protein interaction and a co-expression network.
Inverse scattering problem for quantum graph vertices
Czech Academy of Sciences Publication Activity Database
Cheon, T.; Exner, Pavel; Turek, O.
2011-01-01
Roč. 83, č. 6 (2011), 062715/1-062715/4 ISSN 1050-2947 R&D Projects: GA MŠk LC06002; GA ČR GAP203/11/0701 Institutional research plan: CEZ:AV0Z10480505 Keywords : WIRES Subject RIV: BH - Optics, Masers, Lasers Impact factor: 2.878, year: 2011
A COMBINATORIAL PROBLEM ON A DIRECTED GRAPH
Directory of Open Access Journals (Sweden)
Osvaldo Marrero
2016-08-01
Full Text Available We consider two options for a particle’s entire journey through a certaindirectedgraph. Both options involve a random assignment to the journey route to be followed. We are interested in the option that offers, on average, the shortest route. Therefore, we determine the average journey length for each of the two options. As part of our analysis, we provesome combinatorial identities that appear to be new. Some suggestions for further work are given.
Efficient heuristics for the Rural Postman Problem | Groves | ORiON
African Journals Online (AJOL)
A local search framework for the (undirected) Rural Postman Problem (RPP) is presented in this paper. The framework allows local search approaches that have been applied successfully to the well–known Travelling Salesman Problem also to be applied to the RPP. New heuristics for the RPP, based on this framework, ...
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
Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2008-01-01
We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log...
Graph embedding and extensions: a general framework for dimensionality reduction.
Yan, Shuicheng; Xu, Dong; Zhang, Benyu; Zhang, Hong-Jiang; Yang, Qiang; Lin, Stephen
2007-01-01
Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.
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…
Graphs cospectral with a friendship graph or its complement
Directory of Open Access Journals (Sweden)
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
parallel implementations for many key graph algorithms, conversions between tables and graphs and Python language bindings. SNAP is widely deployed...1. We have used Delite to develop a suite of DSLs for data analysis (query processing, machine learning , and graph processing). Approved for Public...range of users, interested in network analysis: support for Python - a major programming language for data scientists, documentation, tutorials, and
An Extension of Proof Graphs for Disjunctive Parameterised Boolean Equation Systems
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Yutaro Nagae
2017-01-01
Full Text Available A parameterised Boolean equation system (PBES is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a datum and returns a Boolean value. The membership problem of PBESs is a problem to decide whether a given element is in the defined set or not, which corresponds to an execution of the program. This paper introduces reduced proof graphs, and studies a technique to solve the membership problem of PBESs, which is undecidable in general, by transforming it into a reduced proof graph. A vertex X(v in a proof graph represents that the data v is in the set X, if the graph satisfies conditions induced from a given PBES. Proof graphs are, however, infinite in general. Thus we introduce vertices each of which stands for a set of vertices of the original ones, which possibly results in a finite graph. For a subclass of disjunctive PBESs, we clarify some conditions which reduced proof graphs should satisfy. We also show some examples having no finite proof graph except for reduced one. We further propose a reduced dependency space, which contains reduced proof graphs as sub-graphs if a proof graph exists. We provide a procedure to construct finite reduced dependency spaces, and show the soundness and completeness of the procedure.
Efficient enumeration of monocyclic chemical graphs with given path frequencies.
Suzuki, Masaki; Nagamochi, Hiroshi; Akutsu, Tatsuya
2014-01-01
The enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics because it leads to a variety of useful applications including structure determination and development of novel chemical compounds. We consider the problem of enumerating chemical graphs with monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors, where a feature vector represents the frequency of the prescribed paths in a chemical compound to be constructed and the set is specified by a pair of upper and lower feature vectors. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending these algorithms to enumeration of chemical graphs with monocyclic structure by designing a fast algorithm for testing uniqueness. The results of computational experiments reveal that the computational efficiency of the new algorithm is as good as those for enumeration of tree-like chemical compounds. We succeed in expanding the class of chemical graphs that are able to be enumerated efficiently.
On bounding the bandwidth of graphs with symmetry
van Dam, E.R.; Sotirov, R.
2015-01-01
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the min-cut problem. Our new semidefinite programming relaxation of the min-cut problem is obtained by strengthening the known semidefinite programming relaxation for the quadratic assignment problem (or
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.
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.
From graphs to tensegrity structures: Geometric and symbolic approaches
de Guzmán, Miguel; Orden, David
2004-01-01
A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in $\\mathbb{R}^d$ (typically $d=2,3$) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbo...
From graphs to tensegrity structures : geometric and symbolic approaches
Guzmán, Miguel de
2006-01-01
A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in Rd (typically d = 2, 3) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbolic approach.
On d-antimagic labelings of plane graphs
Directory of Open Access Journals (Sweden)
Martin Baca
2013-04-01
Full Text Available The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings for several families of plane graphs.
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...
A contribution to queens graphs: A substitution method
DEFF Research Database (Denmark)
Ambrus, G.; Barat, Janos
2006-01-01
that the Cartesian product of an odd cycle and a path is a queens graph. We show that the same does not hold for two odd cycles. The representation of the Cartesian product of an odd cycle and an even cycle remains an open problem. We also prove constructively that any finite subgraph of the rectangular grid...... or the hexagonal grid is a queens graph. Using a small computer search we solve another conjecture of the authors mentioned above, saying that K-3,K-4 minus an edge is a minimal non-queens graph....
Hadwiger's Conjecture and inflations of the Petersen graph
DEFF Research Database (Denmark)
Pedersen, A. S.
2012-01-01
An inflation of a graph G is obtained by replacing vertices in G by disjoint cliques and adding all possible edges between any pair of cliques corresponding to adjacent vertices in G. We prove that the chromatic number of an arbitrary inflation F of the Petersen graph is equal to the chromatic nu...... number of some inflated 5-cycle contained in F. As a corollary, we find that Hadwiger's Conjecture holds for any inflation of the Petersen graph. This solves a problem posed by Bjarne loft. (C) 2012 Elsevier B.V. All rights reserved....
On domination multisubdivision number of unicyclic graphs
Directory of Open Access Journals (Sweden)
Joanna Raczek
2018-01-01
Full Text Available The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009, 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.
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.
Local graph cut criterion for supervised dimensionality reduction
Zhang, Xiangrong; Zhou, Sisi; Jiao, Licheng
2009-10-01
Graph cut criterion has been proven to be robust and applicable in clustering problems. In this paper the graph cut criterion is applied to construct a supervised dimensionality reduction. A new graph cut, scaling cut, is proposed based on the classical normalized cut. Scaling cut depicts the relationship between samples, which makes it can handle the heteroscedastic and multimodel data in which LDA fails. Meanwhile, the solution to scaling cut is global optimal for it is a generalized eigenvalue problem. To obtain a more reasonable projection matrix and reduce the computational complexity as well, the localized k-nearest neighbor graph is introduced in, which leads to equivalent or better results compared with scaling cut.
Burleigh, Scott C.
2011-01-01
Contact Graph Routing (CGR) is a dynamic routing system that computes routes through a time-varying topology of scheduled communication contacts in a network based on the DTN (Delay-Tolerant Networking) architecture. It is designed to enable dynamic selection of data transmission routes in a space network based on DTN. This dynamic responsiveness in route computation should be significantly more effective and less expensive than static routing, increasing total data return while at the same time reducing mission operations cost and risk. The basic strategy of CGR is to take advantage of the fact that, since flight mission communication operations are planned in detail, the communication routes between any pair of bundle agents in a population of nodes that have all been informed of one another's plans can be inferred from those plans rather than discovered via dialogue (which is impractical over long one-way-light-time space links). Messages that convey this planning information are used to construct contact graphs (time-varying models of network connectivity) from which CGR automatically computes efficient routes for bundles. Automatic route selection increases the flexibility and resilience of the space network, simplifying cross-support and reducing mission management costs. Note that there are no routing tables in Contact Graph Routing. The best route for a bundle destined for a given node may routinely be different from the best route for a different bundle destined for the same node, depending on bundle priority, bundle expiration time, and changes in the current lengths of transmission queues for neighboring nodes; routes must be computed individually for each bundle, from the Bundle Protocol agent's current network connectivity model for the bundle s destination node (the contact graph). Clearly this places a premium on optimizing the implementation of the route computation algorithm. The scalability of CGR to very large networks remains a research topic
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.
Graph Design via Convex Optimization: Online and Distributed Perspectives
Meng, De
Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation
Local adjacency metric dimension of sun graph and stacked book graph
Yulisda Badri, Alifiah; Darmaji
2018-03-01
A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.
Nested Dynamic Condition Response Graphs
DEFF Research Database (Denmark)
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...... Exformatics, a danish provider of case and workflow management systems. We formalize the semantics by giving first a map from Nested to (flat) DCR Graphs with milestones, and then extending the previously given mapping from DCR Graphs to Buchi-automata to include the milestone relation....
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.
How Symmetric Are Real-World Graphs? A Large-Scale Study
Directory of Open Access Journals (Sweden)
Fabian Ball
2018-01-01
Full Text Available The analysis of symmetry is a main principle in natural sciences, especially physics. For network sciences, for example, in social sciences, computer science and data science, only a few small-scale studies of the symmetry of complex real-world graphs exist. Graph symmetry is a topic rooted in mathematics and is not yet well-received and applied in practice. This article underlines the importance of analyzing symmetry by showing the existence of symmetry in real-world graphs. An analysis of over 1500 graph datasets from the meta-repository networkrepository.com is carried out and a normalized version of the “network redundancy” measure is presented. It quantifies graph symmetry in terms of the number of orbits of the symmetry group from zero (no symmetries to one (completely symmetric, and improves the recognition of asymmetric graphs. Over 70% of the analyzed graphs contain symmetries (i.e., graph automorphisms, independent of size and modularity. Therefore, we conclude that real-world graphs are likely to contain symmetries. This contribution is the first larger-scale study of symmetry in graphs and it shows the necessity of handling symmetry in data analysis: The existence of symmetries in graphs is the cause of two problems in graph clustering we are aware of, namely, the existence of multiple equivalent solutions with the same value of the clustering criterion and, secondly, the inability of all standard partition-comparison measures of cluster analysis to identify automorphic partitions as equivalent.
ILIGRA : An Efficient Inverse Line Graph Algorithm
Liu, D.; Trajanovski, S.; Van Mieghem, P.
2014-01-01
This paper presents a new and efficient algorithm, ILIGRA, for inverse line graph construction. Given a line graph H, ILIGRA constructs its root graph G with the time complexity being linear in the number of nodes in H. If ILIGRA does not know whether the given graph H is a line graph, it firstly
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2010-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also outline how to inter......-derive a third style of graph reduction: a graph evaluator....
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Broumi, Said; Talea, Mohamed; Bakali, Assia; Smarandache, Florentin
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Using Graph Transformations and Graph Abstractions for Software Verification
Zambon, Eduardo; Ehrig, Hartmut; Rensink, Arend; Rozenberg, Grzegorz; Schurr, Andy
In this abstract we present an overview of our intended approach for the verification of software written in imperative programming languages. This approach is based on model checking of graph transition systems (GTS), where each program state is modeled as a graph and the exploration engine is
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
We define the -repetition of to be the graph obtained by joining y i to x j for each i ∈ V ( T ) and each child of . In this paper, we compute the Kirchhoff index of the -repetition of in terms of parameters of and . Also we study how K f ( G ) behaves under some graph operations such as joining vertices or ...
Range charts and no-space graphs
Edwards, L.E.
1978-01-01
No-space graphs present one solution to the familiar problem: given data on the occurrence of fossil taxa in separate, well-sampled sections, determine a range chart; that is, a reasonable working hypothesis of the total range in the area in question of each taxon studied. The solution presented here treats only the relative sequence of biostratigraphic events (first and last occurrences of taxa) and does not attempt to determine an amount of spacing between events. Relative to a hypothesized sequence, observed events in any section may be in-place or out-of-place. Out-of-place events may indicate (1) the event in question reflects a taxon that did not fill its entire range (unfilled-range event), or (2) the event in question indicates a need for the revision of the hypothesized sequence. A graph of relative position only (no-space graph) can be used to facilitate the recognition of in-place and out-of-place events by presenting a visual comparison of the observations from each section with the hypothesized sequence. The geometry of the graph as constructed here is such that in-place events will lie along a line series and out-of-place events will lie above or below it. First-occurrence events below the line series and last-occurrence events above the line series indicate unfilled ranges. First-occurrence events above the line series and last-occurrence events below the line series indicate a need for the revision of the hypothesis. Knowing this, the stratigrapher considers alternative positionings of the line series as alternative range hypotheses and seeks the line series that best fits his geologic and paleontologic judgment. No-space graphs are used to revise an initial hypothesis until a final hypothesis is reached. In this final hypothesis every event is found in-place in at least one section, and all events in all sections may be interpreted to represent in-place events or unfilled-range events. No event may indicate a need for further range revision. The
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.
Graphs and matroids weighted in a bounded incline algebra.
Lu, Ling-Xia; Zhang, Bei
2014-01-01
Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.
Applied and computational harmonic analysis on graphs and networks
Irion, Jeff; Saito, Naoki
2015-09-01
In recent years, the advent of new sensor technologies and social network infrastructure has provided huge opportunities and challenges for analyzing data recorded on such networks. In the case of data on regular lattices, computational harmonic analysis tools such as the Fourier and wavelet transforms have well-developed theories and proven track records of success. It is therefore quite important to extend such tools from the classical setting of regular lattices to the more general setting of graphs and networks. In this article, we first review basics of graph Laplacian matrices, whose eigenpairs are often interpreted as the frequencies and the Fourier basis vectors on a given graph. We point out, however, that such an interpretation is misleading unless the underlying graph is either an unweighted path or cycle. We then discuss our recent effort of constructing multiscale basis dictionaries on a graph, including the Hierarchical Graph Laplacian Eigenbasis Dictionary and the Generalized Haar-Walsh Wavelet Packet Dictionary, which are viewed as generalizations of the classical hierarchical block DCTs and the Haar-Walsh wavelet packets, respectively, to the graph setting. Finally, we demonstrate the usefulness of our dictionaries by using them to simultaneously segment and denoise 1-D noisy signals sampled on regular lattices, a problem where classical tools have difficulty.
Label Information Guided Graph Construction for Semi-Supervised Learning.
Zhuang, Liansheng; Zhou, Zihan; Gao, Shenghua; Yin, Jingwen; Lin, Zhouchen; Ma, Yi
2017-09-01
In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks.
Fast construction of voxel-level functional connectivity graphs.
Loewe, Kristian; Grueschow, Marcus; Stoppel, Christian M; Kruse, Rudolf; Borgelt, Christian
2014-06-19
Graph-based analysis of fMRI data has recently emerged as a promising approach to study brain networks. Based on the assessment of synchronous fMRI activity at separate brain sites, functional connectivity graphs are constructed and analyzed using graph-theoretical concepts. Most previous studies investigated region-level graphs, which are computationally inexpensive, but bring along the problem of choosing sensible regions and involve blurring of more detailed information. In contrast, voxel-level graphs provide the finest granularity attainable from the data, enabling analyses at superior spatial resolution. They are, however, associated with considerable computational demands, which can render high-resolution analyses infeasible. In response, many existing studies investigating functional connectivity at the voxel-level reduced the computational burden by sacrificing spatial resolution. Here, a novel, time-efficient method for graph construction is presented that retains the original spatial resolution. Performance gains are instead achieved through data reduction in the temporal domain based on dichotomization of voxel time series combined with tetrachoric correlation estimation and efficient implementation. By comparison with graph construction based on Pearson's r, the technique used by the majority of previous studies, we find that the novel approach produces highly similar results an order of magnitude faster. Its demonstrated performance makes the proposed approach a sensible and efficient alternative to customary practice. An open source software package containing the created programs is freely available for download.
Resonances and poles in isoscattering microwave networks and graphs.
Ławniczak, Michał; Sawicki, Adam; Bauch, Szymon; Kuś, Marek; Sirko, Leszek
2014-03-01
Can one hear the shape of a graph? This is a modification of the famous question of Mark Kac "Can one hear the shape of a drum?" which can be asked in the case of scattering systems such as quantum graphs and microwave networks. It addresses an important mathematical problem whether scattering properties of such systems are uniquely connected to their shapes? Recent experimental results based on a characteristics of graphs such as the cumulative phase of the determinant of the scattering matrices indicate a negative answer to this question [O. Hul, M. Ławniczak, S. Bauch, A. Sawicki, M. Kuś, and L. Sirko, Phys. Rev. Lett. 109, 040402 (2012)]. In this paper we consider important local characteristics of graphs such as structures of resonances and poles of the determinant of the scattering matrices. Using these characteristics we study experimentally and theoretically properties of graphs and directly confirm that the pair of graphs considered in the cited paper is isoscattering. The experimental results are compared to the theoretical ones for a broad frequency range from 0.01 to 3 GHz. In the numerical calculations of the resonances of the graphs absorption present in the experimental networks is taken into account.
Optimal graph based segmentation using flow lines with application to airway wall segmentation
DEFF Research Database (Denmark)
Petersen, Jens; Nielsen, Mads; Lo, Pechin Chien Pau
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited for ...
Optimal graph based segmentation using flow lines with application to airway wall segmentation
DEFF Research Database (Denmark)
Petersen, Jens; Nielsen, Mads; Lo, Pechin
2011-01-01
This paper introduces a novel optimal graph construction method that is applicable to multi-dimensional, multi-surface segmentation problems. Such problems are often solved by refining an initial coarse surface within the space given by graph columns. Conventional columns are not well suited...
DYNAMICALLY MAINTAINING THE VISIBILITY GRAPH
VEGTER, G
1991-01-01
An algorithm is presented to maintain the visibility graph of a set of N line segments in the plane in O(log2 N + K log N) time, where K is the total number of arcs of the visibility graph that are destroyed or created upon insertion or deletion of a line segment. The line segments should be
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)
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
The planar cubic cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Hoede, C.; Liu, X
1998-01-01
In continuation of the paper of Hoede and Li on word graphs for a set of prepositions, word graphs are given for adjectives, adverbs and Chinese classifier words. It is argued that these three classes of words belong to a general class of words that may be called adwords. These words express the
2005-06-01
relationship, trust, etc.) between people. • User Psychology : Clickstream graphs are bipartite graphs connecting Internet users to the websites they visit...document groups (say, science fiction novels and thrillers ), based on the word groups that occur most frequently in them. A user who prefers one
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)
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
theory by defining submanifolds weakly associated with graphs. We prove that, in a local sense, every submanifold satisfies such an association, and other general results. Finally, we study submanifolds associated with graphs either in low dimensions or belonging to some special families. Keywords. Almost Hermitian ...
Eshach, Haim
2010-01-01
One essential skill that students who learn physics should possess is the ability to create and interpret kinematic graphs. However, it is well documented in the literature that students show lack of competence in these abilities. They have problems in connecting graphs and physics concepts, as well as graphs and the real world. The present paper…
Graph-related optimization and decision support systems
Krichen, Saoussen
2014-01-01
Constrained optimization is a challenging branch of operations research that aims to create a model which has a wide range of applications in the supply chain, telecommunications and medical fields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by the system constraints. The aim of this book is expose optimization problems that can be expressed as graphs, by detailing, for each studied problem, the set of nodes and the set of edges. This graph modeling is an incentive for designing a platform that integrates all optimizatio
A Collection of Features for Semantic Graphs
Energy Technology Data Exchange (ETDEWEB)
Eliassi-Rad, T; Fodor, I K; Gallagher, B
2007-05-02
Semantic graphs are commonly used to represent data from one or more data sources. Such graphs extend traditional graphs by imposing types on both nodes and links. This type information defines permissible links among specified nodes and can be represented as a graph commonly referred to as an ontology or schema graph. Figure 1 depicts an ontology graph for data from National Association of Securities Dealers. Each node type and link type may also have a list of attributes. To capture the increased complexity of semantic graphs, concepts derived for standard graphs have to be extended. This document explains briefly features commonly used to characterize graphs, and their extensions to semantic graphs. This document is divided into two sections. Section 2 contains the feature descriptions for static graphs. Section 3 extends the features for semantic graphs that vary over time.
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Quantum chaos on discrete graphs
Energy Technology Data Exchange (ETDEWEB)
Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel); Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH (United Kingdom)
2007-07-06
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral {zeta} functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of {zeta} functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
Dynamic graphs, community detection, and Riemannian geometry
Energy Technology Data Exchange (ETDEWEB)
Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun
2018-03-29
A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.
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 ...
Coined quantum walks on weighted graphs
Wong, Thomas G.
2017-11-01
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy’s quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover’s algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when l < 3 + 2\\sqrt{2} ≈ 5.828 .
Directory of Open Access Journals (Sweden)
I. Sahul Hamid
2016-07-01
Full Text Available A set D of vertices of a graph G is called a dominating set of G if every vertex in V(G−D is adjacent to a vertex in D. A dominating set S such that the subgraph 〈S〉 induced by S has at least one isolated vertex is called an isolate dominating set. An isolate dominating set none of whose proper subset is an isolate dominating set is a minimal isolate dominating set. The minimum and maximum cardinality of a minimal isolate dominating set are called the isolate domination number γ0 and the upper isolate domination number Γ0 respectively. In this paper we initiate a study on these parameters.
Environmental evolutionary graph theory.
Maciejewski, Wes; Puleo, Gregory J
2014-11-07
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have received relatively less attention. Here we present a structured population model where different individuals are best suited to different regions of their environment. The underlying structure is a graph: individuals occupy vertices, which are connected by edges. If an individual is suited for their vertex, they receive an increase in fecundity. This framework allows attention to be restricted to the spatial arrangement of suitable habitat. We prove some basic properties of this model and find some counter-intuitive results. Notably, (1) the arrangement of suitable sites is as important as their proportion, and (2) decreasing the proportion of suitable sites may result in a decrease in the fixation time of an allele. Copyright © 2014 Elsevier Ltd. All rights reserved.
On characterizing terrain visibility graphs
Directory of Open Access Journals (Sweden)
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
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.
Dim target detection method based on salient graph fusion
Hu, Ruo-lan; Shen, Yi-yan; Jiang, Jun
2018-02-01
Dim target detection is one key problem in digital image processing field. With development of multi-spectrum imaging sensor, it becomes a trend to improve the performance of dim target detection by fusing the information from different spectral images. In this paper, one dim target detection method based on salient graph fusion was proposed. In the method, Gabor filter with multi-direction and contrast filter with multi-scale were combined to construct salient graph from digital image. And then, the maximum salience fusion strategy was designed to fuse the salient graph from different spectral images. Top-hat filter was used to detect dim target from the fusion salient graph. Experimental results show that proposal method improved the probability of target detection and reduced the probability of false alarm on clutter background images.
A Graph Based Backtracking Algorithm for Solving General CSPs
Pang, Wanlin; Goodwin, Scott D.
2003-01-01
Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.
Hyperspectral image classification through bilayer graph-based learning.
Gao, Yue; Ji, Rongrong; Cui, Peng; Dai, Qionghai; Hua, Gang
2014-07-01
Hyperspectral image classification with limited number of labeled pixels is a challenging task. In this paper, we propose a bilayer graph-based learning framework to address this problem. For graph-based classification, how to establish the neighboring relationship among the pixels from the high dimensional features is the key toward a successful classification. Our graph learning algorithm contains two layers. The first-layer constructs a simple graph, where each vertex denotes one pixel and the edge weight encodes the similarity between two pixels. Unsupervised learning is then conducted to estimate the grouping relations among different pixels. These relations are subsequently fed into the second layer to form a hypergraph structure, on top of which, semisupervised transductive learning is conducted to obtain the final classification results. Our experiments on three data sets demonstrate the merits of our proposed approach, which compares favorably with state of the art.
Fuzzy Risk Graph Model for Determining Safety Integrity Level
Directory of Open Access Journals (Sweden)
R. Nait-Said
2008-01-01
Full Text Available The risk graph is one of the most popular methods used to determine the safety integrity level for safety instrumented functions. However, conventional risk graph as described in the IEC 61508 standard is subjective and suffers from an interpretation problem of risk parameters. Thus, it can lead to inconsistent outcomes that may result in conservative SIL's. To overcome this difficulty, a modified risk graph using fuzzy rule-based system is proposed. This novel version of risk graph uses fuzzy scales to assess risk parameters, and calibration may be made by varying risk parameter values. Furthermore, the outcomes which are numerical values of risk reduction factor (the inverse of the probability of failure on demand can be compared directly with those given by quantitative and semiquantitative methods such as fault tree analysis (FTA, quantitative risk assessment (QRA, and layers of protection analysis (LOPA.
Modified risk graph method using fuzzy rule-based approach
Energy Technology Data Exchange (ETDEWEB)
Nait-Said, R., E-mail: r_nait_said@hotmail.com [LARPI Laboratory, Safety Department, Institute of Health and Occupational Safety, University of Batna, Road Med El-Hadi Boukhlouf, Batna (Algeria); Zidani, F., E-mail: fati_zidani@lycos.com [LSPIE Laboratory, Electrical Engineering Department, Faculty of Engineering, University of Batna, Road Med El-Hadi Boukhlouf, Batna 05000 (Algeria); Ouzraoui, N., E-mail: ouzraoui@yahoo.fr [LARPI Laboratory, Safety Department, Institute of Health and Occupational Safety, University of Batna, Road Med El-Hadi Boukhlouf, Batna (Algeria)
2009-05-30
The risk graph is one of the most popular methods used to determine the safety integrity level for safety instrumented functions. However, conventional risk graph as described in the IEC 61508 standard is subjective and suffers from an interpretation problem of risk parameters. Thus, it can lead to inconsistent outcomes that may result in conservative SILs. To overcome this difficulty, a modified risk graph using fuzzy rule-based system is proposed. This novel version of risk graph uses fuzzy scales to assess risk parameters and calibration may be made by varying risk parameter values. Furthermore, the outcomes which are numerical values of risk reduction factor (the inverse of the probability of failure on demand) can be compared directly with those given by quantitative and semi-quantitative methods such as fault tree analysis (FTA), quantitative risk assessment (QRA) and layers of protection analysis (LOPA).
CUBu: Universal Real-Time Bundling for Large Graphs.
van der Zwan, Matthew; Codreanu, Valeriu; Telea, Alexandru
2016-12-01
Visualizing very large graphs by edge bundling is a promising method, yet subject to several challenges: speed, clutter, level-of-detail, and parameter control. We present CUBu, a framework that addresses the above problems in an integrated way. Fully GPU-based, CUBu bundles graphs of up to a million edges at interactive framerates, being over 50 times faster than comparable state-of-the-art methods, and has a simple and intuitive control of bundling parameters. CUBu extends and unifies existing bundling techniques, offering ways to control bundle shapes, separate bundles by edge direction, and shade bundles to create a level-of-detail visualization that shows both the graph core structure and its details. We demonstrate CUBu on several large graphs extracted from real-life application domains.
Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.
Mutimbu, Lawrence; Robles-Kelly, Antonio
2016-08-31
This paper presents a method to recover a spatially varying illuminant colour estimate from scenes lit by multiple light sources. Starting with the image formation process, we formulate the illuminant recovery problem in a statistically datadriven setting. To do this, we use a factor graph defined across the scale space of the input image. In the graph, we utilise a set of illuminant prototypes computed using a data driven approach. As a result, our method delivers a pixelwise illuminant colour estimate being devoid of libraries or user input. The use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori (MAP) inference process. Moreover, we compute the probability marginals by performing a Delaunay triangulation on our factor graph. We illustrate the utility of our method for pixelwise illuminant colour recovery on widely available datasets and compare against a number of alternatives. We also show sample colour correction results on real-world images.
Modified risk graph method using fuzzy rule-based approach.
Nait-Said, R; Zidani, F; Ouzraoui, N
2009-05-30
The risk graph is one of the most popular methods used to determine the safety integrity level for safety instrumented functions. However, conventional risk graph as described in the IEC 61508 standard is subjective and suffers from an interpretation problem of risk parameters. Thus, it can lead to inconsistent outcomes that may result in conservative SILs. To overcome this difficulty, a modified risk graph using fuzzy rule-based system is proposed. This novel version of risk graph uses fuzzy scales to assess risk parameters and calibration may be made by varying risk parameter values. Furthermore, the outcomes which are numerical values of risk reduction factor (the inverse of the probability of failure on demand) can be compared directly with those given by quantitative and semi-quantitative methods such as fault tree analysis (FTA), quantitative risk assessment (QRA) and layers of protection analysis (LOPA).
Quantum algorithm for identifying hidden polynomial function graphs
T. Decker; J. Draisma (Jan); P. Wocjan
2008-01-01
htmlabstractWe consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem are not restricted to be linear but can also be
Quantum algorithm for identifying hidden polynomial function graphs
T. Decker; J. Draisma (Jan); P. Wocjan
2009-01-01
htmlabstractWe consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem are not restricted to be linear but can also be
On some properties of doughnut graphs
Directory of Open Access Journals (Sweden)
Md. Rezaul Karim
2016-08-01
Full Text Available The class of doughnut graphs is a subclass of 5-connected planar graphs. It is known that a doughnut graph admits a straight-line grid drawing with linear area, the outerplanarity of a doughnut graph is 3, and a doughnut graph is k-partitionable. In this paper we show that a doughnut graph exhibits a recursive structure. We also give an efficient algorithm for finding a shortest path between any pair of vertices in a doughnut graph. We also propose a nice application of a doughnut graph based on its properties.
Completeness and regularity of generalized fuzzy graphs.
Samanta, Sovan; Sarkar, Biswajit; Shin, Dongmin; Pal, Madhumangal
2016-01-01
Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.
Colored graphs and matrix integrals
International Nuclear Information System (INIS)
Artamkin, I.V.
2007-12-01
In this article we discuss two different asymptotic expansions of matrix integrals. The original approach using the so-called Feynman diagram techniques leads to sums over isomorphism classes of ribbon graphs. Asymptotic expansions of more general Gaussian integrals are sums over isomorphism classes of colored graphs without ribbon structure. Here we derive the former expansion from the latter one. This provides an independent proof for the expansion used by Kontsevich. It might be very interesting to compare the algebra arising in these two approaches. The asymptotic expansion using ribbon graphs leads to the tau function of the KDV hierarchy while the sums over colored graphs satisfy simple partial differential equations which generalize the Burgers equation. We describe the general approach using colored graphs in the second section. In the third section we specialize the results of the second section for the matrix integral. In this section we also derive the expansion over ribbon graphs. The proof is based on simple topological considerations which are contained in section 5. In the last section we give an explicit calculation of the first term of the expansion using colored graphs
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.
Identifying vertex covers in graphs
DEFF Research Database (Denmark)
Henning, Michael A.; Yeo, Anders
2012-01-01
An identifying vertex cover in a graph G is a subset T of vertices in G that has a nonempty intersection with every edge of G such that T distinguishes the edges, that is, e∩T ≠ 0 for every edge e in G and e∩T ≠ f∩T for every two distinct edges e and f in G. The identifying vertex cover number TD......(G) of G is the minimum size of an identifying vertex cover in G. We observe that TD(G)+ρ(G) = |V (G)|, where ρ(G) denotes the packing number of G. We conjecture that if G is a graph of order n and size m with maximum degree Δ, then TD(G) ≤(Δ(Δ-1)/ Δ2+1)n + (2/Δ2+1) m. If the conjecture is true......, then the bound is best possible for all Δ ≥ 1. We prove this conjecture when Δ ≥ 1 and G is a Δ-regular graph. The three known Moore graphs of diameter 2, namely the 5-cycle, the Petersen graph and the Hoffman-Singleton graph, are examples of regular graphs that achieves equality in the upper bound. We also...
Wiener index and Diameter of a Planar Graph in Subquadratic Time
DEFF Research Database (Denmark)
Wulff-Nilsen, Christian
2009-01-01
Consider the problem of computing the sum of distances between each pair of vertices of an unweighted graph. This sum is also known as the Wiener index of the graph, a generalization of a definition given by H. Wiener in 1947. A molecular topological index is a value obtained from the graph...... structure of a molecule such that this value (hopefully) correlates with physical and/or chemical properties of the molecule. The Wiener index is perhaps the most studied molecular topological index with more than a thousand publications. It is open whether the Wiener index of a planar graph can be obtained...... in subquadratic time. In my talk, I will solve this open problem by exhibiting an O(n2 log log n / log n) time algorithm, where n is the size of the graph. A simple modification yields an algorithm with the same time bound that computes the diameter (maximum distance between any vertex pair) of a planar graph. I...
XML Graphs in Program Analysis
DEFF Research Database (Denmark)
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...... of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar...... (transformations between XML and non-XML data), and XSLT (stylesheets for transforming XML documents)....
Large networks and graph limits
Lovász, László
2012-01-01
Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. Developing a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as "property testing" in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact for
Kirchhoff index of graphs and some graph operations
Indian Academy of Sciences (India)
Abstract. Let T be a rooted tree, G a connected graph, x,y ∈ V(G) be fixed and Gi's be |V(T )| disjoint copies of G with xi and yi denoting the corresponding copies of x and y in Gi, respectively. We define the T -repetition of G to be the graph obtained by joining yi to xj for each i ∈ V(T ) and each child j of i. In this paper, we ...
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)
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.
Computing strong metric dimension of some special classes of graphs by genetic algorithms
Directory of Open Access Journals (Sweden)
Kratica Jozef
2008-01-01
Full Text Available In this paper we consider the NP-hard problem of determining the strong metric dimension of graphs. The problem is solved by a genetic algorithm that uses binary encoding and standard genetic operators adapted to the problem. This represents the first attempt to solve this problem heuristically. We report experimental results for the two special classes of ORLIB test instances: crew scheduling and graph coloring.
Voice-Centric LTE Femtocells and Improper Graph Colorings
DEFF Research Database (Denmark)
Garcia, Luis Guilherme Uzeda; Pedersen, Klaus; Mogensen, Preben
2012-01-01
This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring. The investig......This paper addresses carrier-based inter-cell interference coordination (CB-ICIC) among LTE femtocells operating on a single carrier. CB-ICIC is in many ways linked to the widely investigated dynamic channel assignment problem, which is often studied in the context of graph coloring...
Open Graphs and Computational Reasoning
Directory of Open Access Journals (Sweden)
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Graph Model Based Indoor Tracking
DEFF Research Database (Denmark)
Jensen, Christian Søndergaard; Lu, Hua; Yang, Bin
2009-01-01
The tracking of the locations of moving objects in large indoor spaces is important, as it enables a range of applications related to, e.g., security and indoor navigation and guidance. This paper presents a graph model based approach to indoor tracking that offers a uniform data management...... infrastructure for different symbolic positioning technologies, e.g., Bluetooth and RFID. More specifically, the paper proposes a model of indoor space that comprises a base graph and mappings that represent the topology of indoor space at different levels. The resulting model can be used for one or several...... indoor positioning technologies. Focusing on RFID-based positioning, an RFID specific reader deployment graph model is built from the base graph model. This model is then used in several algorithms for constructing and refining trajectories from raw RFID readings. Empirical studies with implementations...
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...
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
Leuven: Katholieke Universiteit Leuven). (1990). [5] Etayo F, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen 53 (1998) 217–223. [6] Harary F, Graph Theory (Reading: Addison-Wesley) (1972). [7] Papaghiuc N ...
Graph anomalies in cyber communications
Energy Technology Data Exchange (ETDEWEB)
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Rectilinear Graphs and Angular Resolution
Bodlaender, H.L.; Tel, G.
2003-01-01
In this note we show that a planar graph with angular resolution at least π/2 can be drawn with all angles an integer multiple of π/2, that is, in a rectilinear manner. Moreover, we show that for d ≠ 4, d › 2, having an angular resolution of 2π/d does not imply that the graph can be drawn with all
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.
On dominator colorings in graphs
Indian Academy of Sciences (India)
A dominator coloring of a graph G is a proper coloring of G in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by χd(G). In this paper we present several results on graphs ...
a generalization of total graphs
Indian Academy of Sciences (India)
8
Abstract. Let R be a commutative ring with nonzero identity, Ln(R) be the set of all lower triangular n × n matrices, and U be a triangular subset of. Rn i.e. the product of any lower triangular matrix with the transpose of any element of U, belongs to U. The graph GTn. U (Rn) is a simple graph whose ver- tices consists of all ...
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Summary 2: Graph Grammar Verification through Abstraction
Baldan, P.; Koenig, B.; Rensink, A.; Rensink, Arend; König, B.; Montanari, U.; Gardner, P.
2005-01-01
Until now there have been few contributions concerning the verification of graph grammars, specifically of infinite-state graph grammars. This paper compares two existing approaches, based on abstractions of graph transformation systems. While in the unfolding approach graph grammars are
On Graph Rewriting, Reduction and Evaluation
DEFF Research Database (Denmark)
Zerny, Ian
2009-01-01
We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt. To this end, we adapt Danvy et al.'s mechanical program derivations from the world of terms to the world of graphs. We also inter-derive a graph evaluator....
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…
Regular graph construction for semi-supervised learning
International Nuclear Information System (INIS)
Vega-Oliveros, Didier A; Berton, Lilian; Eberle, Andre Mantini; Lopes, Alneu de Andrade; Zhao, Liang
2014-01-01
Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN
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.
Neuro-symbolic representation learning on biological knowledge graphs
Alshahrani, Mona
2017-04-21
Biological data and knowledge bases increasingly rely on Semantic Web technologies and the use of knowledge graphs for data integration, retrieval and federated queries. In the past years, feature learning methods that are applicable to graph-structured data are becoming available, but have not yet widely been applied and evaluated on structured biological knowledge.We develop a novel method for feature learning on biological knowledge graphs. Our method combines symbolic methods, in particular knowledge representation using symbolic logic and automated reasoning, with neural networks to generate embeddings of nodes that encode for related information within knowledge graphs. Through the use of symbolic logic, these embeddings contain both explicit and implicit information. We apply these embeddings to the prediction of edges in the knowledge graph representing problems of function prediction, finding candidate genes of diseases, protein-protein interactions, or drug target relations, and demonstrate performance that matches and sometimes outperforms traditional approaches based on manually crafted features. Our method can be applied to any biological knowledge graph, and will thereby open up the increasing amount of SemanticWeb based knowledge bases in biology to use in machine learning and data analytics.https://github.com/bio-ontology-research-group/walking-rdf-and-owl.robert.hoehndorf@kaust.edu.sa.Supplementary data are available at Bioinformatics online.
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.
Neuro-symbolic representation learning on biological knowledge graphs.
Alshahrani, Mona; Khan, Mohammad Asif; Maddouri, Omar; Kinjo, Akira R; Queralt-Rosinach, Núria; Hoehndorf, Robert
2017-09-01
Biological data and knowledge bases increasingly rely on Semantic Web technologies and the use of knowledge graphs for data integration, retrieval and federated queries. In the past years, feature learning methods that are applicable to graph-structured data are becoming available, but have not yet widely been applied and evaluated on structured biological knowledge. Results: We develop a novel method for feature learning on biological knowledge graphs. Our method combines symbolic methods, in particular knowledge representation using symbolic logic and automated reasoning, with neural networks to generate embeddings of nodes that encode for related information within knowledge graphs. Through the use of symbolic logic, these embeddings contain both explicit and implicit information. We apply these embeddings to the prediction of edges in the knowledge graph representing problems of function prediction, finding candidate genes of diseases, protein-protein interactions, or drug target relations, and demonstrate performance that matches and sometimes outperforms traditional approaches based on manually crafted features. Our method can be applied to any biological knowledge graph, and will thereby open up the increasing amount of Semantic Web based knowledge bases in biology to use in machine learning and data analytics. https://github.com/bio-ontology-research-group/walking-rdf-and-owl. robert.hoehndorf@kaust.edu.sa. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.
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.
Graph Quasicontinuous Functions and Densely Continuous Forms
Directory of Open Access Journals (Sweden)
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
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
Dynamic programming and graph algorithms in computer vision.
Felzenszwalb, Pedro F; Zabih, Ramin
2011-04-01
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 nontrivial guarantees concerning solution quality. In this paper, we 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.
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
Phage, Itumeleng B.; Lemmer, Miriam; Hitge, Mariette
2017-01-01
Students' graph comprehension may be affected by the background of the students who are the readers or interpreters of the graph, their knowledge of the context in which the graph is set, and the inferential processes required by the graph operation. This research study investigated these aspects of graph comprehension for 152 first year…
Modelling Traffic Flows Using Graph Theory
Directory of Open Access Journals (Sweden)
Oksana Musyt
2011-04-01
Full Text Available An intensive increase in road transport, particularly individual, in recent years has led to such consequences as increased time spent on travel, the number of forced stops, traffic accidents, the occurrence of traffic jams on the road network, reducing traffic speed and a deteriorated urban road network in cities. The most effective method for solving these problems is the use of graph theory, the main characteristics of which is reliability, durability and accessibility of a free as well as loaded network. Based on their analysis the methods for network optimization are proposed.Article in Russian
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
Geometry of Graph Edit Distance Spaces
Jain, Brijnesh J.
2015-01-01
In this paper we study the geometry of graph spaces endowed with a special class of graph edit distances. The focus is on geometrical results useful for statistical pattern recognition. The main result is the Graph Representation Theorem. It states that a graph is a point in some geometrical space, called orbit space. Orbit spaces are well investigated and easier to explore than the original graph space. We derive a number of geometrical results from the orbit space representation, translate ...
GraphMeta: Managing HPC Rich Metadata in Graphs
Energy Technology Data Exchange (ETDEWEB)
Dai, Dong; Chen, Yong; Carns, Philip; Jenkins, John; Zhang, Wei; Ross, Robert
2016-01-01
High-performance computing (HPC) systems face increasingly critical metadata management challenges, especially in the approaching exascale era. These challenges arise not only from exploding metadata volumes, but also from increasingly diverse metadata, which contains data provenance and arbitrary user-defined attributes in addition to traditional POSIX metadata. This ‘rich’ metadata is becoming critical to supporting advanced data management functionality such as data auditing and validation. In our prior work, we identified a graph-based model as a promising solution to uniformly manage HPC rich metadata due to its flexibility and generality. However, at the same time, graph-based HPC rich metadata anagement also introduces significant challenges to the underlying infrastructure. In this study, we first identify the challenges on the underlying infrastructure to support scalable, high-performance rich metadata management. Based on that, we introduce GraphMeta, a graphbased engine designed for this use case. It achieves performance scalability by introducing a new graph partitioning algorithm and a write-optimal storage engine. We evaluate GraphMeta under both synthetic and real HPC metadata workloads, compare it with other approaches, and demonstrate its advantages in terms of efficiency and usability for rich metadata management in HPC systems.
An advance in infinite graph models for the analysis of transportation networks
Directory of Open Access Journals (Sweden)
Cera Martín
2016-12-01
Full Text Available This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximum number of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situations for the finite case. In particular, concepts from ‘finite’ graph theory, like the average degree and the extremal number, are generalized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation of dangerous goods are presented; they involve the analysis of networks and percolation thresholds.
Debnath, Lokenath
2010-01-01
This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…
The Use of Graphs in Specific Situations of the Initial Conditions of Linear Differential Equations
Buendía, Gabriela; Cordero, Francisco
2013-01-01
In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…
Graph theory with applications
Vasudev, C
2006-01-01
Salient Features Over 1500 problems are used to illustrate concepts, related to different topics, and introduce applications. Over 1000 exercises in the text with many different types of questions posed. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements. Problem sets are stated clearly and unambiguously, and all are carefully graded for various levels of difficulty. This text has been carefully designed for flexible use.
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.
Flexible Manifold Learning With Optimal Graph for Image and Video Representation.
Wang, Wei; Yan, Yan; Nie, Feiping; Yan, Shuicheng; Sebe, Nicu
2018-06-01
Graph-based dimensionality reduction techniques have been widely and successfully applied to clustering and classification tasks. The basis of these algorithms is the constructed graph which dictates their performance. In general, the graph is defined by the input affinity matrix. However, the affinity matrix derived from the data is sometimes suboptimal for dimension reduction as the data used are very noisy. To address this issue, we propose the projective unsupervised flexible embedding models with optimal graph (PUFE-OG). We build an optimal graph by adjusting the affinity matrix. To tackle the out-of-sample problem, we employ a linear regression term to learn a projection matrix. The optimal graph and the projection matrix are jointly learned by integrating the manifold regularizer and regression residual into a unified model. The experimental results on the public benchmark datasets demonstrate that the proposed PUFE-OG outperforms state-of-the-art methods.
Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán
2016-07-01
We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation
Bond graph modelling of engineering systems: theory, applications and software support
National Research Council Canada - National Science Library
Borutzky, Wolfgang; Margolis, Donald L
2011-01-01
... way such that analytical or computer response predictions can be straightforwardly carried out. Bond graphs are a concise pictorial representation of all types of interacting energetic systems. In my experience working with engineers on the development of complex systems it is obvious that these systems suffer from thermal problems, structural problems, vibration and noise problems, and control and stability issues that do not fit into a single discipline. Bond graphs provide the link by which all these different ...
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.
Hierarchical organisation of causal graphs
International Nuclear Information System (INIS)
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
An algebraic approach to graph codes
DEFF Research Database (Denmark)
Pinero, Fernando
theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four...... are optimal or best known for their parameters. In chapter five we study some graph codes with Reed–Solomon component codes. The underlying graph is well known and widely used for its good characteristics. This helps us to compute the dimension of the graph codes. We also introduce a combinatorial concept...... related to the iterative encoding of graph codes with MDS component code. The last chapter deals with affine Grassmann codes and Grassmann codes. We begin with some previously known codes and prove that they are also Tanner codes of the incidence graph of the point–line partial geometry...
Combinatorics and graph theory
Vasudev, C
2007-01-01
About the Book: This text has been carefully designed for flexible use for First Semester M.C.A. course of Uttar Pradesh Technical University (U.P.T.U.), and it contains the following features: Precise mathematical language is used without excessive formalism and abstraction. Over 900 exercises (problem sets) in the text with many different types of questions posed. Care has been taken to balance the mix of notation and words in mathematical statements. Problem sets (exercises) are stated clearly and unambiguously and all are carefully graded for various levels of difficulty. Contents:
chromatic number of a complete balanced multipartite graph
African Journals Online (AJOL)
2006-12-29
Dec 29, 2006 ... Geldenhuys, who introduced us to the sheer beauty of graph theory in the early nineteen nineties, and who fostered in us an affinity for hard operations research. Abstract. In this paper we solve (approximately) the problem of finding the minimum number of colours with which the vertices of a complete, ...