Journal articles on the topic 'Graph algorithms'
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Chen, Yuzhong, Zhenyu Liu, Yulin Liu, and Chen Dong. "Distributed Attack Modeling Approach Based on Process Mining and Graph Segmentation." Entropy 22, no. 9 (September 14, 2020): 1026. http://dx.doi.org/10.3390/e22091026.
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Attack graph modeling aims to generate attack models by investigating attack behaviors recorded in intrusion alerts raised in network security devices. Attack models can help network security administrators discover an attack strategy that intruders use to compromise the network and implement a timely response to security threats. However, the state-of-the-art algorithms for attack graph modeling are unable to obtain a high-level or global-oriented view of the attack strategy. To address the aforementioned issue, considering the similarity between attack behavior and workflow, we employ a heuristic process mining algorithm to generate the initial attack graph. Although the initial attack graphs generated by the heuristic process mining algorithm are complete, they are extremely complex for manual analysis. To improve their readability, we propose a graph segmentation algorithm to split a complex attack graph into multiple subgraphs while preserving the original structure. Furthermore, to handle massive volume alert data, we propose a distributed attack graph generation algorithm based on Hadoop MapReduce and a distributed attack graph segmentation algorithm based on Spark GraphX. Additionally, we conduct comprehensive experiments to validate the performance of the proposed algorithms. The experimental results demonstrate that the proposed algorithms achieve considerable improvement over comparative algorithms in terms of accuracy and efficiency.
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Ji, Shengwei, Chenyang Bu, Lei Li, and Xindong Wu. "Local Graph Edge Partitioning." ACM Transactions on Intelligent Systems and Technology 12, no. 5 (October 31, 2021): 1–25. http://dx.doi.org/10.1145/3466685.
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Graph edge partitioning, which is essential for the efficiency of distributed graph computation systems, divides a graph into several balanced partitions within a given size to minimize the number of vertices to be cut. Existing graph partitioning models can be classified into two categories: offline and streaming graph partitioning models. The former requires global graph information during the partitioning, which is expensive in terms of time and memory for large-scale graphs. The latter creates partitions based solely on the received graph information. However, the streaming model may result in a lower partitioning quality compared with the offline model. Therefore, this study introduces a Local Graph Edge Partitioning model, which considers only the local information (i.e., a portion of a graph instead of the entire graph) during the partitioning. Considering only the local graph information is meaningful because acquiring complete information for large-scale graphs is expensive. Based on the Local Graph Edge Partitioning model, two local graph edge partitioning algorithms—Two-stage Local Partitioning and Adaptive Local Partitioning—are given. Experimental results obtained on 14 real-world graphs demonstrate that the proposed algorithms outperform rival algorithms in most tested cases. Furthermore, the proposed algorithms are proven to significantly improve the efficiency of the real graph computation system GraphX.
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Li, Jonathan, Rohan Potru, and Farhad Shahrokhi. "A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph." Algorithms 13, no. 12 (December 14, 2020): 339. http://dx.doi.org/10.3390/a13120339.
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We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices.
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Dib, Fadi K., and Peter Rodgers. "Graph drawing using Jaya." PLOS ONE 18, no. 6 (June 27, 2023): e0287744. http://dx.doi.org/10.1371/journal.pone.0287744.
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Graph drawing, involving the automatic layout of graphs, is vital for clear data visualization and interpretation but poses challenges due to the optimization of a multi-metric objective function, an area where current search-based methods seek improvement. In this paper, we investigate the performance of Jaya algorithm for automatic graph layout with straight lines. Jaya algorithm has not been previously used in the field of graph drawing. Unlike most population-based methods, Jaya algorithm is a parameter-less algorithm in that it requires no algorithm-specific control parameters and only population size and number of iterations need to be specified, which makes it easy for researchers to apply in the field. To improve Jaya algorithm’s performance, we applied Latin Hypercube Sampling to initialize the population of individuals so that they widely cover the search space. We developed a visualization tool that simplifies the integration of search methods, allowing for easy performance testing of algorithms on graphs with weighted aesthetic metrics. We benchmarked the Jaya algorithm and its enhanced version against Hill Climbing and Simulated Annealing, commonly used graph-drawing search algorithms which have a limited number of parameters, to demonstrate Jaya algorithm’s effectiveness in the field. We conducted experiments on synthetic datasets with varying numbers of nodes and edges using the Erdős–Rényi model and real-world graph datasets and evaluated the quality of the generated layouts, and the performance of the methods based on number of function evaluations. We also conducted a scalability experiment on Jaya algorithm to evaluate its ability to handle large-scale graphs. Our results showed that Jaya algorithm significantly outperforms Hill Climbing and Simulated Annealing in terms of the quality of the generated graph layouts and the speed at which the layouts were produced. Using improved population sampling generated better layouts compared to the original Jaya algorithm using the same number of function evaluations. Moreover, Jaya algorithm was able to draw layouts for graphs with 500 nodes in a reasonable time.
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SKULRATTANAKULCHAI, SAN, and HAROLD N. GABOW. "COLORING ALGORITHMS ON SUBCUBIC GRAPHS." International Journal of Foundations of Computer Science 15, no. 01 (February 2004): 21–40. http://dx.doi.org/10.1142/s0129054104002285.
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We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/ log n) processors and runs in O( log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.
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RAJASEKARAN, SANGUTHEVAR, and VAMSI KUNDETI. "SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM." International Journal of Foundations of Computer Science 20, no. 03 (June 2009): 479–99. http://dx.doi.org/10.1142/s0129054109006693.
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The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prove that our algorithms will work on all possible instances. In this paper, we also give a new construction for cospectral graphs.
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Saeed, Ayesha, Ali Husnain, Anam Zahoor, and Mehmood Gondal. "A Comparative Study of Cat Swarm Algorithm for Graph Coloring Problem: Convergence Analysis and Performance Evaluation." International Journal of Innovative Research in Computer Science and Technology 12, no. 4 (July 2024): 1–9. http://dx.doi.org/10.55524/ijircst.2024.12.4.1.
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The Graph Coloring Problem (GCP) is a significant optimization challenge widely suitable to solve scheduling problems. Its goal is to specify the minimum colors (k) required to color a graph properly. Due to its NP-completeness, exact algorithms become impractical for graphs exceeding 100 vertices. As a result, approximation algorithms have gained prominence for tackling large-scale instances. In this context, the Cat Swarm algorithm, a novel population-based metaheuristic in the domain of swarm intelligence, has demonstrated promising convergence properties compared to other population-based algorithms. This research focuses on designing and implementing the Cat Swarm algorithm to address the GCP. By conducting a comparative study with established algorithms, our investigation revolves around quantifying the minimum value of k required by the Cat Swarm algorithm for each graph instance. The evaluation metrics include the algorithm's running time in seconds, success rate, and the mean count of iterations or assessments required to reach a goal.
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Serratosa, Francesc. "A Methodology to Generate Attributed Graphs with a Bounded Graph Edit Distance for Graph-Matching Testing." International Journal of Pattern Recognition and Artificial Intelligence 32, no. 11 (July 24, 2018): 1850038. http://dx.doi.org/10.1142/s0218001418500386.
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This paper presents a methodology for generating pairs of attributed graphs with a lower and upper- bounded graph edit distance (GED). It is independent of the type of attributes on nodes and edges. The algorithm is composed of three steps: randomly generating a graph, generating another graph as a sub-graph of the first, and adding structural and semantic noise to both. These graphs, together with their bounded distances, can be used to manufacture synthetic databases of large graphs. The exact GED between large graphs cannot be obtained for runtime reasons since it has to be computed through an optimal algorithm with an exponential computational cost. Through this database, we can test the behavior of the known or new sub-optimal error-tolerant graph-matching algorithms against a lower and an upper bound GED on large graphs, even though we do not have the true distance. It is not clear how the error induced by the use of sub-optimal algorithms grows with problem size. Thus, with this methodology, we can generate graph databases and analyze if the current assumption that we can extrapolate algorithms’ behavior from matching small graphs to large graphs is correct or not. We also show that with some restrictions, the methodology returns the optimal GED in a quadratic time and that it can also be used to generate graph databases to test exact sub-graph isomorphism algorithms.
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Manaster, Alfred B., Jeffrey B. Remmel, and James H. Schmerl. "Planarity and minimal path algorithms." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 131–42. http://dx.doi.org/10.1017/s1446788700026550.
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AbstractIn 1981 two notions of effective presentation of countable connected graphs were formulated by J. C. E. Dekker—namely, edge recognition algorithm graphs and minimal path algorithm graphs. In this paper we show that every planar graph has a minimal path algorithm presentation but that some graphs have no minimal path algorithm presentations. We introduce the notion of a shortest distance algorithm graph, show that it lies strictly between the two notions of Dekker, and show that every graph has a shortest distance algorithm presentation. Finally, in contrast to Dekker's result about minimal path algorithm graphs, we produce a shortest distance algorithm graph which has no spanning tree which is an edge recognition algorithm graph.
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GODDARD, WAYNE, STEPHEN T. HEDETNIEMI, DAVID P. JACOBS, and PRADIP K. SRIMANI. "SELF-STABILIZING ALGORITHMS FOR ORDERINGS AND COLORINGS." International Journal of Foundations of Computer Science 16, no. 01 (February 2005): 19–36. http://dx.doi.org/10.1142/s012905410500284x.
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A k-forward numbering of a graph is a labeling of the nodes with integers such that each node has less than k neighbors whose labels are equal or larger. Distributed algorithms that reach a legitimate state, starting from any illegitimate state, are called self-stabilizing. We obtain three self-stabilizing (s-s) algorithms for finding a k-forward numbering, provided one exists. One such algorithm also finds the k-height numbering of graph, generalizing s-s algorithms by Bruell et al. [4] and Antonoiu et al. [1] for finding the center of a tree. Another k-forward numbering algorithm runs in polynomial time. The motivation of k-forward numberings is to obtain new s-s graph coloring algorithms. We use a k-forward numbering algorithm to obtain an s-s algorithm that is more general than previous coloring algorithms in the literature, and which k-colors any graph having a k-forward numbering. Special cases of the algorithm 6-color planar graphs, thus generalizing an s-s algorithm by Ghosh and Karaata [13], as well as 2-color trees and 3-color series-parallel graphs. We discuss how our s-s algorithms can be extended to the synchronous model.
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Bera, Abhijit, Mrinal Kanti Ghose, and Dibyendu Kumar Pal. "Graph Classification Using Back Propagation Learning Algorithms." International Journal of Systems and Software Security and Protection 11, no. 2 (July 2020): 1–12. http://dx.doi.org/10.4018/ijsssp.2020070101.
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Due to the propagation of graph data, there has been a sharp focus on developing effective methods for classifying the graph object. As most of the proposed graph classification techniques though effective are constrained by high computational overhead, there is a consistent effort to improve upon the existing classification algorithms in terms of higher accuracy and less computational time. In this paper, an attempt has been made to classify graphs by extracting various features and selecting the important features using feature selection algorithms. Since all the extracted graph-based features need not be equally important, only the most important features are selected by using back propagation learning algorithm. The results of the proposed study of feature-based approach using back propagation learning algorithm lead to higher classification accuracy with faster computational time in comparison to other graph kernels. It also appears to be more effective for large unlabeled graphs.
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Chang, Xian, Jordan Eizenga, Adam M. Novak, Jouni Sirén, and Benedict Paten. "Distance indexing and seed clustering in sequence graphs." Bioinformatics 36, Supplement_1 (July 1, 2020): i146—i153. http://dx.doi.org/10.1093/bioinformatics/btaa446.
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Abstract Motivation Graph representations of genomes are capable of expressing more genetic variation and can therefore better represent a population than standard linear genomes. However, due to the greater complexity of genome graphs relative to linear genomes, some functions that are trivial on linear genomes become much more difficult in genome graphs. Calculating distance is one such function that is simple in a linear genome but complicated in a graph context. In read mapping algorithms such distance calculations are fundamental to determining if seed alignments could belong to the same mapping. Results We have developed an algorithm for quickly calculating the minimum distance between positions on a sequence graph using a minimum distance index. We have also developed an algorithm that uses the distance index to cluster seeds on a graph. We demonstrate that our implementations of these algorithms are efficient and practical to use for a new generation of mapping algorithms based upon genome graphs. Availability and implementation Our algorithms have been implemented as part of the vg toolkit and are available at https://github.com/vgteam/vg.
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Chen, Yuhan, Haojie Ye, Sanketh Vedula, Alex Bronstein, Ronald Dreslinski, Trevor Mudge, and Nishil Talati. "Demystifying Graph Sparsification Algorithms in Graph Properties Preservation." Proceedings of the VLDB Endowment 17, no. 3 (November 2023): 427–40. http://dx.doi.org/10.14778/3632093.3632106.
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Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the downstream task while minimizing the graph's size. Graph algorithms often suffer from long execution time due to the irregularity and the large real-world graph size. Graph sparsification can be applied to greatly reduce the run time of graph algorithms by substituting the full graph with a much smaller sparsified graph, without significantly degrading the output quality. However, the interaction between numerous sparsifiers and graph properties is not widely explored, and the potential of graph sparsification is not fully understood. In this work, we cover 16 widely-used graph metrics, 12 representative graph sparsification algorithms, and 14 real-world input graphs spanning various categories, exhibiting diverse characteristics, sizes, and densities. We developed a framework to extensively assess the performance of these sparsification algorithms against graph metrics, and provide insights to the results. Our study shows that there is no one sparsifier that performs the best in preserving all graph properties, e.g. sparsifiers that preserve distance-related graph properties (eccentricity) struggle to perform well on Graph Neural Networks (GNN). This paper presents a comprehensive experimental study evaluating the performance of sparsification algorithms in preserving essential graph metrics. The insights inform future research in incorporating matching graph sparsification to graph algorithms to maximize benefits while minimizing quality degradation. Furthermore, we provide a framework to facilitate the future evaluation of evolving sparsification algorithms, graph metrics, and ever-growing graph data.
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Şeker, Oylum, Pinar Heggernes, Tinaz Ekim, and Z. Caner Taşkın. "Generation of random chordal graphs using subtrees of a tree." RAIRO - Operations Research 56, no. 2 (March 2022): 565–82. http://dx.doi.org/10.1051/ro/2022027.
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Chordal graphs form one of the most studied graph classes. Several graph problems that are NP-hard in general become solvable in polynomial time on chordal graphs, whereas many others remain NP-hard. For a large group of problems among the latter, approximation algorithms, parameterized algorithms, and algorithms with moderately exponential or sub-exponential running time have been designed. Chordal graphs have also gained increasing interest during the recent years in the area of enumeration algorithms. Being able to test these algorithms on instances of chordal graphs is crucial for understanding the concepts of tractability of hard problems on graph classes. Unfortunately, only few published papers give algorithms for generating chordal graphs. Even in these papers, only very few methods aim for generating a large variety of chordal graphs. Surprisingly, none of these methods is directly based on the “intersection of subtrees of a tree” characterization of chordal graphs. In this paper, we give an algorithm for generating chordal graphs, based on the characterization that a graph is chordal if and only if it is the intersection graph of subtrees of a tree. Upon generating a random host tree, we give and test various methods that generate subtrees of the host tree. We compare our methods to one another and to existing ones for generating chordal graphs. Our experiments show that one of our methods is able to generate the largest variety of chordal graphs in terms of maximal clique sizes. Moreover, two of our subtree generation methods result in an overall complexity of our generation algorithm that is the best possible time complexity for a method generating the entire node set of subtrees in an “intersection of subtrees of a tree” representation. The instances corresponding to the results presented in this paper, and also a set of relatively small-sized instances are made available online.
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Rautiainen, Mikko, Veli Mäkinen, and Tobias Marschall. "Bit-parallel sequence-to-graph alignment." Bioinformatics 35, no. 19 (March 9, 2019): 3599–607. http://dx.doi.org/10.1093/bioinformatics/btz162.
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Abstract Motivation Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence the genetic variation present in a population. Being able to align sequencing reads to such graphs is a key step for many analyses and its applications include genome assembly, read error correction and variant calling with respect to a variation graph. Results We generalize two linear sequence-to-sequence algorithms to graphs: the Shift-And algorithm for exact matching and Myers’ bitvector algorithm for semi-global alignment. These linear algorithms are both based on processing w sequence characters with a constant number of operations, where w is the word size of the machine (commonly 64), and achieve a speedup of up to w over naive algorithms. For a graph with |V| nodes and |E| edges and a sequence of length m, our bitvector-based graph alignment algorithm reaches a worst case runtime of O(|V|+⌈mw⌉|E| log w) for acyclic graphs and O(|V|+m|E| log w) for arbitrary cyclic graphs. We apply it to five different types of graphs and observe a speedup between 3-fold and 20-fold compared with a previous (asymptotically optimal) alignment algorithm. Availability and implementation https://github.com/maickrau/GraphAligner Supplementary information Supplementary data are available at Bioinformatics online.
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Kralev, Velin, and Radoslava Kraleva. "An analysis between different algorithms for the graph vertex coloring problem." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 3 (June 1, 2023): 2972. http://dx.doi.org/10.11591/ijece.v13i3.pp2972-2980.
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<span lang="EN-US">This research focuses on an analysis of different algorithms for the graph vertex coloring problem. Some approaches to solving the problem are discussed. Moreover, some studies for the problem and several methods for its solution are analyzed as well. An exact algorithm (using the backtracking method) is presented. The complexity analysis of the algorithm is discussed. Determining the average execution time of the exact algorithm is consistent with the multitasking mode of the operating system. This algorithm generates optimal solutions for all studied graphs. In addition, two heuristic algorithms for solving the graph vertex coloring problem are used as well. The results show that the exact algorithm can be used to solve the graph vertex coloring problem for small graphs with 30-35 vertices. For half of the graphs, all three algorithms have found the optimal solutions. The suboptimal solutions generated by the approximate algorithms are identical in terms of the number of colors needed to color the corresponding graphs. The results show that the linear increase in the number of vertices and edges of the analyzed graphs causes a linear increase in the number of colors needed to color these graphs.</span>
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NASTOS, JAMES, and YONG GAO. "BOUNDED SEARCH TREE ALGORITHMS FOR PARAMETRIZED COGRAPH DELETION: EFFICIENT BRANCHING RULES BY EXPLOITING STRUCTURES OF SPECIAL GRAPH CLASSES." Discrete Mathematics, Algorithms and Applications 04, no. 01 (March 2012): 1250008. http://dx.doi.org/10.1142/s1793830912500085.
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Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general search strategy that branches on the forbidden subgraphs of a graph class relaxation. By using the class of P4-sparse graphs as the relaxed graph class, we obtain efficient bounded search tree algorithms for several parametrized deletion problems. We give the first non-trivial bounded search tree algorithms for the cograph edge-deletion problem and the trivially perfect edge-deletion problems. For the cograph vertex deletion problem, a refined analysis of the runtime of our simple bounded search algorithm gives a faster exponential factor than those algorithms designed with the help of complicated case distinctions and non-trivial running time analysis [R. Niedermeier and P. Rossmanith, An efficient fixed-parameter algorithm for 3-hitting set, J. Discrete Algorithms1(1) (2003) 89–102] and computer-aided branching rules [J. Gramm, J. Guo, F. Hüffner and R. Niedermeier, Automated generation of search tree algorithms for hard graph modification problems, Algorithmica39(4) (2004) 321–347].
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ERWIG, MARTIN. "Inductive graphs and functional graph algorithms." Journal of Functional Programming 11, no. 5 (August 29, 2001): 467–92. http://dx.doi.org/10.1017/s0956796801004075.
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We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functional-style graph algorithms instead of the imperative algorithms that are dominant today.
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Kralev, Velin, Radoslava Kraleva, and Viktor Ankov. "An Interactive Application for Learning and Analyzing Different Graph Vertex Cover Algorithms." International Journal of Engineering Pedagogy (iJEP) 13, no. 1 (February 16, 2023): 4–19. http://dx.doi.org/10.3991/ijep.v13i1.35661.
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This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially.
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Danilov, I. G., and S. I. Rodzin. "Distributed implementation of the graphs clusterization goodness metrics calculation using mapreduce and vertex-oriented graph processing model." Informatization and communication, no. 3 (May 5, 2020): 31–35. http://dx.doi.org/10.34219/2078-8320-2020-11-3-31-35.
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Goal. Research of the implementation features of the graph clusterization goodness metrics using the vertexoriented graph computing model and MapReduce. Materials and methods. The basic concepts of graph theory were used to define the goodness metrics, and the MapReduce with a vertex-oriented graph-computational approach were used to develop the goodness metrics calculation algorithms. Results. Distributed algorithms for calculating graph clustering goodness metrics are proposed and tested. Conclusion. The results can be used to analyze the quality of the partitioning of large graphs that obtained using an arbitrary distributed clustering algorithm.
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LAVRENCHUK, Svitlana, Nina ZDOLBITSKA, and Nadiia KHAMULA. "SOFTWARE COMPLEX FOR GRAPH ALGORITHMS VISUALIZATION." Herald of Khmelnytskyi National University 303, no. 6 (December 2021): 81–85. http://dx.doi.org/10.31891/2307-5732-2021-303-6-81-85.
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Algorithms on graphs represented by graphical structures are offered. The software complex has a modular web interface. A representative graph is implemented as a set of vertices in the form of numbered circles and links between them (graphic image); using dynamically linked lists (adjacency lists); using an adjacency matrix. The project of this project allows the use of interactive algorithms for step-by-step calculations and algorithms on graphical images to obtain the necessary research results and competencies in the use of discrete structures. The project was implemented using HTML, CSS, JavaScript, which allows visualizing the application and interactively working with algorithms on graphs represented by different data structures. Graphics File Algorithm Programming provides web-based and interactive algorithms created by the used DHTML itself, creating a software project in the form of a site. Each page is dedicated to a separate algorithm and structurally consists of a header, container, footer. The website design uses HTML and cascading CSS stylesheets, to create an interactive parsing process and to transform methods in graphic files – based on JavaScript, which allows third-party scripts to be processed and rendered. The user can vibrate the image type (for orientation), the number of nodes, the presentation method, generate this graph, indicate the starting point for starting the search algorithm, observe the operational operation of the algorithm. The user can adjust the animation speed. The development of a set of programs is meant for interactive demonstration and visualization of the operation of algorithms in the study of graph theory.
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GAVRIL, FANICA. "ALGORITHMS ON SUBGRAPH OVERLAP GRAPHS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450018. http://dx.doi.org/10.1142/s1793830914500189.
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Consider a graph D and a family FI of connected edge subgraphs of D. Let GI(V, F) be the intersection graph of FI and G the overlap graph of FI. We describe polynomial time algorithms for subgraph overlap graphs G when their intersection graphs GI have specific hereditary properties. The algorithms are to find maximum induced complete bipartite subgraphs, maximum weight holes of a given parity, minimum dominating holes, antiholes of a given parity and some others. In addition, we define the family of subgraph filament graphs based on D, FI and GI, and prove it to be the same as the family of subgraph overlap graphs.
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Shiau, S. Y., R. Joynt, and S. N. Coppersmith. "Physically-motivated dynamical algorithms for the graph isomorphism problem." Quantum Information and Computation 5, no. 6 (September 2005): 492–506. http://dx.doi.org/10.26421/qic5.6-7.
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The graph isomorphism problem (GI) plays a central role in the theory of computational complexity and has importance in physics and chemistry as well \cite{kobler93,fortin96}. No polynomial-time algorithm for solving GI is known. We investigate classical and quantum physics-based polynomial-time algorithms for solving the graph isomorphism problem in which the graph structure is reflected in the behavior of a dynamical system. We show that a classical dynamical algorithm proposed by Gudkov and Nussinov \cite{gudkov02} as well as its simplest quantum generalization fail to distinguish pairs of non-isomorphic strongly regular graphs. However, by combining the algorithm of Gudkov and Nussinov with a construction proposed by Rudolph \cite{rudolph02} in which one examines a graph describing the dynamics of two particles on the original graph, we find an algorithm that successfully distinguishes all pairs of non-isomorphic strongly regular graphs that we tested with up to 29 vertices.
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Cusack, Charles A., Aaron Green, Airat Bekmetjev, and Mark Powers. "Graph pebbling algorithms and Lemke graphs." Discrete Applied Mathematics 262 (June 2019): 72–82. http://dx.doi.org/10.1016/j.dam.2019.02.028.
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Zhang, Rener. "The comparison of three MST algorithms." Applied and Computational Engineering 17, no. 1 (October 23, 2023): 191–97. http://dx.doi.org/10.54254/2755-2721/17/20230939.
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The minimum spanning tree, connecting all the nodes of a connected, weighted graph with the minimum possible total edge weight, is a fundamental concept of graph theory. Thus, how to find the minimum spanning tree (MST) with higher efficiency appears to be crucial. Three kinds of algorithms for this problem have already been developed: Kruskal, Prim, Boruvka. In order to make readers have a better understanding of the three algorithms in the process of studying and teaching, this paper uses the method of comparing to indicate the differences and commonalities between these three algorithms, draws a conclusion afterwards, and points out the most suitable situations to apply them in the end: Kruskals algorithm is suitable in sparse graphs while Prims algorithm and Boruvkas algorithm are suitable in dense graphs.
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Fava, Leandro, João Furtado, Gilson Helfer, Jorge Barbosa, Marko Beko, Sérgio Correia, and Valderi Leithardt. "A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints." Symmetry 13, no. 9 (September 14, 2021): 1697. http://dx.doi.org/10.3390/sym13091697.
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This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.
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Agrawal, Garima, Dimitri Bertsekas, and Huan Liu. "Auction-Based Learning for Question Answering over Knowledge Graphs." Information 14, no. 6 (June 15, 2023): 336. http://dx.doi.org/10.3390/info14060336.
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Knowledge graphs are graph-based data models which can represent real-time data that is constantly growing with the addition of new information. The question-answering systems over knowledge graphs (KGQA) retrieve answers to a natural language question from the knowledge graph. Most existing KGQA systems use static knowledge bases for offline training. After deployment, they fail to learn from unseen new entities added to the graph. There is a need for dynamic algorithms which can adapt to the evolving graphs and give interpretable results. In this research work, we propose using new auction algorithms for question answering over knowledge graphs. These algorithms can adapt to changing environments in real-time, making them suitable for offline and online training. An auction algorithm computes paths connecting an origin node to one or more destination nodes in a directed graph and uses node prices to guide the search for the path. The prices are initially assigned arbitrarily and updated dynamically based on defined rules. The algorithm navigates the graph from the high-price to the low-price nodes. When new nodes and edges are dynamically added or removed in an evolving knowledge graph, the algorithm can adapt by reusing the prices of existing nodes and assigning arbitrary prices to the new nodes. For subsequent related searches, the “learned” prices provide the means to “transfer knowledge” and act as a “guide: to steer it toward the lower-priced nodes. Our approach reduces the search computational effort by 60% in our experiments, thus making the algorithm computationally efficient. The resulting path given by the algorithm can be mapped to the attributes of entities and relations in knowledge graphs to provide an explainable answer to the query. We discuss some applications for which our method can be used.
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Zhang, Lixia, and Jianliang Gao. "Incremental Graph Pattern Matching Algorithm for Big Graph Data." Scientific Programming 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6749561.
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Graph pattern matching is widely used in big data applications. However, real-world graphs are usually huge and dynamic. A small change in the data graph or pattern graph could cause serious computing cost. Incremental graph matching algorithms can avoid recomputing on the whole graph and reduce the computing cost when the data graph or the pattern graph is updated. The existing incremental algorithm PGC_IncGPM can effectively reduce matching time when no more than half edges of the pattern graph are updated. However, as the number of changed edges increases, the improvement of PGC_IncGPM gradually decreases. To solve this problem, an improved algorithm iDeltaP_IncGPM is developed in this paper. For multiple insertions (resp., deletions) on pattern graphs, iDeltaP_IncGPM determines the nodes’ matching state detection sequence and processes them together. Experimental results show that iDeltaP_IncGPM has higher efficiency and wider application range than PGC_IncGPM.
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Mateescu, R., K. Kask, V. Gogate, and R. Dechter. "Join-Graph Propagation Algorithms." Journal of Artificial Intelligence Research 37 (March 17, 2010): 279–328. http://dx.doi.org/10.1613/jair.2842.
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The paper investigates parameterized approximate message-passing schemes that are based on bounded inference and are inspired by Pearls belief propagation algorithm (BP). We start with the bounded inference mini-clustering algorithm and then move to the iterative scheme called Iterative Join-Graph Propagation (IJGP), that combines both iteration and bounded inference. Algorithm IJGP belongs to the class of Generalized Belief Propagation algorithms, a framework that allowed connections with approximate algorithms from statistical physics and is shown empirically to surpass the performance of mini-clustering and belief propagation, as well as a number of other state-of-the-art algorithms on several classes of networks. We also provide insight into the accuracy of iterative BP and IJGP by relating these algorithms to well known classes of constraint propagation schemes.
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SOHAEE, NASSIM, and CHRISTIAN V. FORST. "IDENTIFICATION OF FUNCTIONAL MODULES IN A PPI NETWORK BY BOUNDED DIAMETER CLUSTERING." Journal of Bioinformatics and Computational Biology 08, no. 06 (December 2010): 929–43. http://dx.doi.org/10.1142/s0219720010005221.
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Dense subgraphs of Protein–Protein Interaction (PPI) graphs are assumed to be potential functional modules and play an important role in inferring the functional behavior of proteins. Increasing amount of available PPI data implies a fast, accurate approach of biological complex identification. Therefore, there are different models and algorithms in identifying functional modules. This paper describes a new graph theoretic clustering algorithm that detects densely connected regions in a large PPI graph. The method is based on finding bounded diameter subgraphs around a seed node. The algorithm has the advantage of being very simple and efficient when compared with other graph clustering methods. This algorithm is tested on the yeast PPI graph and the results are compared with MCL, Core-Attachment, and MCODE algorithms.
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Gargi, Ullas, Wenjun Lu, Vahab Mirrokni, and Sangho Yoon. "Large-Scale Community Detection on YouTube for Topic Discovery and Exploration." Proceedings of the International AAAI Conference on Web and Social Media 5, no. 1 (August 3, 2021): 486–89. http://dx.doi.org/10.1609/icwsm.v5i1.14191.
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Detecting coherent, well-connected communities in large graphs provides insight into the graph structure and can serve as the basis for content discovery. Clustering is a popular technique for community detection but global algorithms that examine the entire graph do not scale. Local algorithms are highly parallelizable but perform sub-optimally, especially in applications where we need to optimize multiple metrics. We present a multi-stage algorithm based on local-clustering that is highly scalable, combining a pre-processing stage, a lo- cal clustering stage, and a post-processing stage. We apply it to the YouTube video graph to generate named clusters of videos with coherent content. We formalize coverage, co- herence, and connectivity metrics and evaluate the quality of the algorithm for large YouTube graphs. Our use of local algorithms for global clustering, and its implementation and practical evaluation on such a large scale is a first of its kind.
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SINHA, DEEPA, and DEEPAKSHI SHARMA. "On Square and 2-path Signed Graph." Journal of Interconnection Networks 16, no. 01 (March 2016): 1550011. http://dx.doi.org/10.1142/s0219265915500115.
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A signed graph is an ordered pair [Formula: see text], where [Formula: see text] is a graph G = (V, E), called the underlying graph of S and [Formula: see text] is a function from the edge set E of Su into the set {+, -}, called the signature of S. In this paper, we characterize all those signed graphs whose 2-path signed graphs are isomorphic to their square signed graph along with algorithm to check the same. In other sections we find the characterization of signed graph S such that [Formula: see text] where D is a derived signed graph of the signed graph S such as: line signed graphs, total signed graphs, common edge signed graphs, splitting signed graphs. Also each characterization is supported by algorithms for the same.
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Talmaciu, Mihai, and Elena Nechita. "On Polar, Trivially Perfect Graphs." International Journal of Computers Communications & Control 5, no. 5 (December 1, 2010): 939. http://dx.doi.org/10.15837/ijccc.2010.5.2257.
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<p>During the last decades, different types of decompositions have been processed in the field of graph theory. In various problems, for example in the construction of recognition algorithms, frequently appears the so-called weakly decomposition of graphs.<br />Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. Recognizing a polar graph is known to be NP-complete. For this class of graphs, polynomial algorithms for the maximum stable set problem are unknown and algorithms for the dominating set problem are also NP-complete.<br />In this paper we characterize the polar graphs using the weakly decomposition, give a polynomial time algorithm for recognizing graphs that are both trivially perfect and polar, and directly calculate the domination number. For the stability number and clique number, we give polynomial time algorithms. </p>
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Reba, Kristjan, Matej Guid, Kati Rozman, Dušanka Janežič, and Janez Konc. "Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning." Mathematics 10, no. 1 (December 28, 2021): 97. http://dx.doi.org/10.3390/math10010097.
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Finding a maximum clique is important in research areas such as computational chemistry, social network analysis, and bioinformatics. It is possible to compare the maximum clique size between protein graphs to determine their similarity and function. In this paper, improvements based on machine learning (ML) are added to a dynamic algorithm for finding the maximum clique in a protein graph, Maximum Clique Dynamic (MaxCliqueDyn; short: MCQD). This algorithm was published in 2007 and has been widely used in bioinformatics since then. It uses an empirically determined parameter, Tlimit, that determines the algorithm’s flow. We have extended the MCQD algorithm with an initial phase of a machine learning-based prediction of the Tlimit parameter that is best suited for each input graph. Such adaptability to graph types based on state-of-the-art machine learning is a novel approach that has not been used in most graph-theoretic algorithms. We show empirically that the resulting new algorithm MCQD-ML improves search speed on certain types of graphs, in particular molecular docking graphs used in drug design where they determine energetically favorable conformations of small molecules in a protein binding site. In such cases, the speed-up is twofold.
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Chu, Deming, Fan Zhang, Wenjie Zhang, Ying Zhang, and Xuemin Lin. "Graph Summarization: Compactness Meets Efficiency." Proceedings of the ACM on Management of Data 2, no. 3 (May 29, 2024): 1–26. http://dx.doi.org/10.1145/3654943.
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As the volume and ubiquity of graphs increase, a compact graph representation becomes essential for enabling efficient storage, transfer, and processing of graphs. Given a graph, the graph summarization problem asks for a compact representation that consists of a summary graph and the corrections, such that we can recreate the original graph from the representation exactly. Although this problem has been studied extensively, the existing works either trade summary compactness for efficiency, or vice versa. In particular, a well-known greedy method provides the most compact summary but incurs prohibitive time cost, while the state-of-the-art algorithms with practical overheads are more than 20% behind in summary compactness in our comparison with the greedy method. This paper presents Mags and Mags-DM, two algorithms that aim to bridge the compactness and efficiency in graph summarization. Mags adopts the existing greedy paradigm that provides state-of-the-art compactness, but significantly improves its efficiency with a novel algorithm design. Meanwhile, Mags-DM follows a different paradigm with practical efficiency and overcomes its limitations in compactness. Moreover, both algorithms can support parallel computing environments. We evaluate Mags and Mags-DM on graphs up to billion-scale and demonstrate that they achieve state-of-the-art in both compactness and efficiency, rather than in one of them. Compared with the method that offers state-of-the-art compactness, Mags and Mags-DM have a small difference (< 0.1% and < 2.1%) in compactness. For efficiency, Mags is on average 11.1x and 4.2x faster than the two state-of-the-art algorithms with practical overheads, while Mags-DM can further reduce the running time by 13.4x compared with Mags. This shows that graph summarization algorithms can be made practical while still offering a compact summary.
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Eshaghian, Mary Mehrnoosh. "MAPPING ARBITRARY HETEROGENEOUS TASK GRAPHS ONTO ARBITRARY HETEROGENEOUS SYSTEM GRAPH." International Journal of Foundations of Computer Science 12, no. 05 (October 2001): 599–628. http://dx.doi.org/10.1142/s0129054101000680.
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In this paper, a generic technique for mapping arbitrary heterogeneous task graphs onto arbitrary heterogeneous system graphs is presented. The heterogeneous task and system graphs studied in this paper have nonuniform computation and communication weights associated with the nodes and the edges. Two clustering algorithms have been proposed that can be used to obtain a multilayer clustered graph called a Spec graph from a given task graph and a multilayer clustered graph called a Rep graph from a given system graph. We present a mapping algorithm that produces a suboptimal matching of a given Spec graph containing M task modules onto a Rep graph of N processors, in O(M2) time, where N ≤ M. Our experimental results indicate that our mapping algorithm is the fastest one and generates results that are better than, or similar to, those of other leading techniques, some of which work only for restricted task or system graphs.
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Krishnaa, Auparajita. "Some Algorithms of Graph Theory in Cryptology." Indian Journal of Advanced Mathematics 4, no. 1 (April 30, 2024): 9–15. http://dx.doi.org/10.54105/ijam.a1167.04010424.
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The inventive use of concepts from Graph Theory plays a significant role in hiding the original Plain-text for resulting in a significantly safe data transfer. In this work, the tree traversal algorithms like Inorder, Preorder, Postorder, Kruskal’s algorithm for making minimal spanning tree and the modified graph labelling scheme of graceful labelling allowing repetition of exactly one vertex label for certain graphs, have been employed to create highly hidden Cipher-texts. Encryption and decryption algorithms for all these methods are being presented in this work.
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Kása, Zoltán, Pál A. Kupán, and Csaba György Pătcaş. "Methods for the graph realization problem." Acta Universitatis Sapientiae, Informatica 15, no. 2 (December 1, 2023): 267–93. http://dx.doi.org/10.2478/ausi-2023-0017.
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Abstract The graph realization problem seeks an answer to how and under what conditions a graph can be constructed if we know the degrees of its vertices. The problem was widely studied by many authors and in many ways, but there are still new ideas and solutions. In this sense, the paper presents the known necessary and su cient conditions for realization with the description in pseudocode of the corresponding algorithms. Two cases to solve the realization problem are treated: finding one solution, and finding all solutions. In this latter case a parallel approach is presented too, and how to exclude isomorphic graphs from solutions. We are also discussing algorithms using binary integer programming and flow networks. In the case of a bigraphical list with equal out- and in-degree sequences a modified Edmonds–Karp algorithm is presented such that the resulting graph will be always symmetric without containing loops. This algorithm solves the problem of graph realization in the case of undirected graphs using flow networks.
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Dhulipala, Laxman, Guy E. Blelloch, and Julian Shun. "Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable." ACM Transactions on Parallel Computing 8, no. 1 (April 2021): 1–70. http://dx.doi.org/10.1145/3434393.
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There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the interfaces, optimizations, and graph processing techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph Based Benchmark Suite (GBBS).
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Kenyeres, Martin, and Jozef Kenyeres. "Distributed Average Consensus Algorithms in d-Regular Bipartite Graphs: Comparative Study." Future Internet 15, no. 5 (May 16, 2023): 183. http://dx.doi.org/10.3390/fi15050183.
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Consensus-based data aggregation in d-regular bipartite graphs poses a challenging task for the scientific community since some of these algorithms diverge in this critical graph topology. Nevertheless, one can see a lack of scientific studies dealing with this topic in the literature. Motivated by our recent research concerned with this issue, we provide a comparative study of frequently applied consensus algorithms for distributed averaging in d-regular bipartite graphs in this paper. More specifically, we examine the performance of these algorithms with bounded execution in this topology in order to identify which algorithm can achieve the consensus despite no reconfiguration and find the best-performing algorithm in these graphs. In the experimental part, we apply the number of iterations required for consensus to evaluate the performance of the algorithms in randomly generated regular bipartite graphs with various connectivities and for three configurations of the applied stopping criterion, allowing us to identify the optimal distributed consensus algorithm for this graph topology. Moreover, the obtained experimental results presented in this paper are compared to other scientific manuscripts where the analyzed algorithms are examined in non-regular non-bipartite topologies.
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Kim, Jaehyeon, Sejong Lee, Yushin Kim, Seyoung Ahn, and Sunghyun Cho. "Graph Learning-Based Blockchain Phishing Account Detection with a Heterogeneous Transaction Graph." Sensors 23, no. 1 (January 1, 2023): 463. http://dx.doi.org/10.3390/s23010463.
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Recently, cybercrimes that exploit the anonymity of blockchain are increasing. They steal blockchain users’ assets, threaten the network’s reliability, and destabilize the blockchain network. Therefore, it is necessary to detect blockchain cybercriminal accounts to protect users’ assets and sustain the blockchain ecosystem. Many studies have been conducted to detect cybercriminal accounts in the blockchain network. They represented blockchain transaction records as homogeneous transaction graphs that have a multi-edge. They also adopted graph learning algorithms to analyze transaction graphs. However, most graph learning algorithms are not efficient in multi-edge graphs, and homogeneous graphs ignore the heterogeneity of the blockchain network. In this paper, we propose a novel heterogeneous graph structure called an account-transaction graph, ATGraph. ATGraph represents a multi-edge as single edges by considering transactions as nodes. It allows graph learning more efficiently by eliminating multi-edges. Moreover, we compare the performance of ATGraph with homogeneous transaction graphs in various graph learning algorithms. The experimental results demonstrate that the detection performance using ATGraph as input outperforms that using homogeneous graphs as the input by up to 0.2 AUROC.
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FANKHAUSER, STEFAN, KASPAR RIESEN, HORST BUNKE, and PETER DICKINSON. "SUBOPTIMAL GRAPH ISOMORPHISM USING BIPARTITE MATCHING." International Journal of Pattern Recognition and Artificial Intelligence 26, no. 06 (September 2012): 1250013. http://dx.doi.org/10.1142/s0218001412500139.
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Graphs provide us with a flexible and powerful way to represent objects in various areas of computer science. One of the main drawbacks is, however, that many standard algorithms on graphs have a high computational complexity. The present paper considers the problem of graph isomorphism, i.e. checking two graphs for identity. A novel approach for the efficient computation of graph isomorphism is presented. The proposed algorithm is based on bipartite graph matching by means of an assignment algorithm. The algorithmic framework is suboptimal in the sense of possibly rejecting pairs of graphs without making a decision. As an advantage, however, it offers polynomial runtime. In experiments on diverse graph data sets we demonstrate substantial speedups of our proposed method over several standard procedures for graph isomorphism. Furthermore, although the computational framework for isomorphism is suboptimal, we show that the proposed algorithm rejects only very few pairs of graphs and otherwise returns correct results.
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Sarno, Riyanarto, and Kelly Rossa Sungkono. "A survey of graph-based algorithms for discovering business processes." International Journal of Advances in Intelligent Informatics 5, no. 2 (July 30, 2019): 137. http://dx.doi.org/10.26555/ijain.v5i2.296.
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Algorithms of process discovery help analysts to understand business processes and problems in a system by creating a process model based on a log of the system. There are existing algorithms of process discovery, namely graph-based. Of all algorithms, there are algorithms that process graph-database to depict a process model. Those algorithms claimed that those have less time complexity because of the graph-database ability to store relationships. This research analyses graph-based algorithms by measuring the time complexity and performance metrics and comparing them with a widely used algorithm, i.e. Alpha Miner and its expansion. Other than that, this research also gives outline explanations about graph-based algorithms and their focus issues. Based on the evaluations, the graph-based algorithm has high performance and less time complexity than Alpha Miner algorithm.
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Kalenkova, Anna A., and Danil A. Kolesnikov. "Application of Genetic Algorithms for Finding Edit Distance between Process Models." Modeling and Analysis of Information Systems 25, no. 6 (December 19, 2018): 711–25. http://dx.doi.org/10.18255/1818-1015-2018-6-711-725.
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Finding graph-edit distance (graph similarity) is an important task in many computer science areas, such as image analysis, machine learning, chemicalinformatics. Recently, with the development of process mining techniques, it became important to adapt and apply existing graph analysis methods to examine process models (annotated graphs) discovered from event data. In particular, finding graph-edit distance techniques can be used to reveal patterns (subprocesses), compare discovered process models. As it was shown experimentally and theoretically justified, exact methods for finding graph-edit distances between discovered process models (and graphs in general) are computationally expensive and can be applied to small models only. In this paper, we present and assess accuracy and performance characteristics of an inexact genetic algorithm applied to find distances between process models discovered from event logs. In particular, we find distances between BPMN (Business Process Model and Notation) models discovered from event logs by using different process discovery algorithms. We show that the genetic algorithm allows us to dramatically reduce the time of comparison and produces results which are close to the optimal solutions (minimal graph edit distances calculated by the exact search algorithm).
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Talvitie, Topi, and Mikko Koivisto. "Counting and Sampling Markov Equivalent Directed Acyclic Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7984–91. http://dx.doi.org/10.1609/aaai.v33i01.33017984.
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Exploring directed acyclic graphs (DAGs) in a Markov equivalence class is pivotal to infer causal effects or to discover the causal DAG via appropriate interventional data. We consider counting and uniform sampling of DAGs that are Markov equivalent to a given DAG. These problems efficiently reduce to counting the moral acyclic orientations of a given undirected connected chordal graph on n vertices, for which we give two algorithms. Our first algorithm requires O(2nn4) arithmetic operations, improving a previous superexponential upper bound. The second requires O(k!2kk2n) operations, where k is the size of the largest clique in the graph; for bounded-degree graphs this bound is linear in n. After a single run, both algorithms enable uniform sampling from the equivalence class at a computational cost linear in the graph size. Empirical results indicate that our algorithms are superior to previously presented algorithms over a range of inputs; graphs with hundreds of vertices and thousands of edges are processed in a second on a desktop computer.
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Chang, Lijun, Mouyi Xu, and Darren Strash. "Efficient maximum k -plex computation over large sparse graphs." Proceedings of the VLDB Endowment 16, no. 2 (October 2022): 127–39. http://dx.doi.org/10.14778/3565816.3565817.
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The k -plex model is a relaxation of the clique model by allowing every vertex to miss up to k neighbors. Designing exact and efficient algorithms for computing a maximum k -plex in a graph has been receiving increasing interest recently. However, the existing algorithms are still inefficient due to having major limitations. We in this paper design a new algorithm kPlexS for the maximum k -plex problem, with three novel contributions. Firstly, we propose a new framework for computing maximum k -plex over large sparse graphs, by iteratively extracting small dense subgraphs from it and then solving each of the extracted dense subgraphs by a branch-and-bound search. Secondly, we propose an efficient reduction algorithm CTCP to reduce the input graph size by exhaustively conducting vertex reduction and edge reduction. CTCP computes a smaller reduced graph and also has a lower time complexity than the existing techniques. Moreover, we iteratively invoke CTCP to reduce the input graph once a vertex has been processed and removed from it. Thirdly, we develop a branch-and-bound algorithm BBMatrix specifically targeting the dense subgraphs that are extracted from the input graph. BBMatrix represents its input graph by an adjacency matrix, and utilizes both first-order (i.e., individual vertices) and second-order information (i.e., pairs of vertices) for reduction and upper bounding. In addition, incremental techniques are proposed to efficiently apply the reduction and upper bounding during the recursion. Extensive empirical studies on large real graphs demonstrate that our algorithm kPlexS outperforms the state-of-the-art algorithms BnB, Maplex, and KpLeX.
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Schab, Esteban, Carla Casanova, and Fabiana Piccoli. "Graph Representations for Reinforcement Learning." Journal of Computer Science and Technology 24, no. 1 (April 22, 2024): e03. http://dx.doi.org/10.24215/16666038.24.e03.
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Graph analysis is becoming increasingly important due to the expressive power of graph models and the efficient algorithms available for processing them. Reinforcement Learning is one domain that could benefit from advancements in graph analysis, given that a learning agent may be integrated into an environment that can be represented as a graph. Nevertheless, the structural irregularity of graphs and the lack of prior labels make it difficult to integrate such a model into modern Reinforcement Learning frameworks that rely on artificial neural networks. Graph embedding enables the learning of low-dimensional vector representations that are more suited for machine learning algorithms, while retaining essential graph features. This paper presents a framework for evaluating graph embedding algorithms and their ability to preserve the structure and relevant features of graphs by means of an internal validation metric, without resorting to subsequent tasks that require labels for training. Based on this framework, three defined algorithms that meet the necessary requirements for solving a specific problem of Reinforcement Learning in graphs are selected, analyzed, and compared. These algorithms are Graph2Vec, GL2Vec, and Wavelet Characteristics, with the latter two demonstrating superior performance.
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Terra-Neves, Miguel, José Amaral, Alexandre Lemos, Rui Quintino, Pedro Resende, and Antonio Alegria. "SAT-Based Algorithms for Regular Graph Pattern Matching." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 8 (March 24, 2024): 8136–45. http://dx.doi.org/10.1609/aaai.v38i8.28653.
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Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.
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Bahrami, Saeedeh, Alireza Bosaghzadeh, and Fadi Dornaika. "Multi Similarity Metric Fusion in Graph-Based Semi-Supervised Learning." Computation 7, no. 1 (March 7, 2019): 15. http://dx.doi.org/10.3390/computation7010015.
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In semi-supervised label propagation (LP), the data manifold is approximated by a graph, which is considered as a similarity metric. Graph estimation is a crucial task, as it affects the further processes applied on the graph (e.g., LP, classification). As our knowledge of data is limited, a single approximation cannot easily find the appropriate graph, so in line with this, multiple graphs are constructed. Recently, multi-metric fusion techniques have been used to construct more accurate graphs which better represent the data manifold and, hence, improve the performance of LP. However, most of these algorithms disregard use of the information of label space in the LP process. In this article, we propose a new multi-metric graph-fusion method, based on the Flexible Manifold Embedding algorithm. Our proposed method represents a unified framework that merges two phases: graph fusion and LP. Based on one available view, different simple graphs were efficiently generated and used as input to our proposed fusion approach. Moreover, our method incorporated the label space information as a new form of graph, namely the Correlation Graph, with other similarity graphs. Furthermore, it updated the correlation graph to find a better representation of the data manifold. Our experimental results on four face datasets in face recognition demonstrated the superiority of the proposed method compared to other state-of-the-art algorithms.
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Kralev, Velin, and Radoslava Kraleva. "A comparative analysis between two heuristic algorithms for the graph vertex coloring problem." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 3 (June 1, 2023): 2981. http://dx.doi.org/10.11591/ijece.v13i3.pp2981-2989.
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This study focuses on two heuristic algorithms for the graph vertex coloring problem: the sequential (greedy) coloring algorithm (SCA) and the Welsh–Powell algorithm (WPA). The code of the algorithms is presented and discussed. The methodology and conditions of the experiments are presented. The execution time of the algorithms was calculated as the average of four different starts of the algorithms for all analyzed graphs, taking into consideration the multitasking mode of the operating system. In the graphs with less than 600 vertices, in 90% of cases, both algorithms generated the same solutions. In only 10% of cases, the WPA algorithm generates better solutions. However, in the graphs with more than 1,000 vertices, in 35% of cases, the WPA algorithm generates better solutions. The results show that the difference in the execution time of the algorithms for all graphs is acceptable, but the quality of the solutions generated by the WPA algorithm in more than 20% of cases is better compared to the SC algorithm. The results also show that the quality of the solutions is not related to the number of iterations performed by the algorithms.