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Fast maximum clique algorithms for large graphs

Ryan A. Rossi, David F. Gleich, Assefaw H. Gebremedhin, Md. Mostofa Ali Patwary
2014 Proceedings of the 23rd International Conference on World Wide Web - WWW '14 Companion  
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks.  ...  Key to the efficiency of our algorithm are an initial heuristic procedure that finds a large clique quickly and a parallelized branch and bound strategy with aggressive pruning and ordering techniques.  ...  ALGORITHMS AND APPLICATIONS We propose a fast, parallel maximum clique finder wellsuited for applications involving large sparse graphs.  ... 
doi:10.1145/2567948.2577283 dblp:conf/www/RossiGGP14 fatcat:euicae4rqzcapbjzxvaxwencke

Parallel Maximum Clique Algorithms with Applications to Network Analysis

Ryan A. Rossi, David F. Gleich, Assefaw H. Gebremedhin
2015 SIAM Journal on Scientific Computing  
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks.  ...  During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search  ...  As a result one is inclined to believe that exact algorithms for finding maximum cliques will be too slow to be practical for large network analysis applications.  ... 
doi:10.1137/14100018x fatcat:6enika5twfgl7ccu2jbwumzemm

A Fast Heuristic Algorithm Based on Verification and Elimination Methods for Maximum Clique Problem [article]

Murali Krishna P, Sabu .M Thampi
2007 arXiv   pre-print
We have succeeded in developing a fast algorithm for maximum clique problem by employing the method of verification and elimination.  ...  The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is NP-Complete.  ...  This necessitates the development of fast and approximate algorithms for the problem.  ... 
arXiv:0710.0748v1 fatcat:pore6jioenhilb6i5l2b7mdp4i

Approximate Maximum Clique Algorithm (AMCA): A Clever Technique for Solving the Maximum Clique Problem through Near Optimal Algorithm for Minimum Vertex Cover Problem

Muhammad Fayaz, Shakeel Arshad, Abdul Salam Shah, Asadullah Shah
2018 International Journal of Control and Automation  
The only way left is to use the approximation algorithm of Minimum Vertex Cover (MVC) for the solution of the Maximum Clique (MC) problem.  ...  Results: The development of an efficient approximation algorithm for the Maximum Clique (MC) problem is very difficult due to its complex nature.  ...  The method either returns the optimal result of the maximum clique problem or reduces the graph for maximum clique algorithms.  ... 
doi:10.14257/ijca.2018.11.3.04 fatcat:irnddjzbrngolmdert2qiamfrm

Solving large Maximum Clique problems on a quantum annealer [article]

Elijah Pelofske, Georg Hahn, Hristo N. Djidjev
2019 arXiv   pre-print
For the important Maximum Clique problem, this article investigates methods for decomposing larger problem instances into smaller ones, which can subsequently be solved on D-Wave.  ...  The reduction methods presented in this article include upper and lower bound heuristics in conjunction with graph decomposition, vertex and edge extraction, and persistency analysis.  ...  In comparison, our algorithm is top-down, starting with the original graph and splitting it down to smaller graphs, which are examined for a maximum clique.  ... 
arXiv:1901.07657v3 fatcat:fm5gwmnwhrdtxa3tp72pzpj5ne

Fast Algorithms for the Maximum Clique Problem on Massive Sparse Graphs [article]

Bharath Pattabiraman, Md. Mostofa Ali Patwary, Assefaw H. Gebremedhin, Wei-keng Liao, Alok Choudhary
2012 arXiv   pre-print
We present a new exact algorithm that employs novel pruning techniques to very quickly find maximum cliques in large sparse graphs.  ...  Although there exist several algorithms with acceptable runtimes for certain classes of graphs, many of them are infeasible for massive graphs.  ...  Algorithm 2 Heuristic for finding the maximum clique in a graph. Input: Graph G = (V, E).  ... 
arXiv:1209.5818v4 fatcat:67sqkj5h7rf6bfjzn7xpgiai2a

What if CLIQUE were fast? Maximum Cliques in Information Networks and Strong Components in Temporal Networks [article]

Ryan A. Rossi, David F. Gleich, Assefaw H. Gebremedhin, Md. Mostofa Ali Patwary
2012 arXiv   pre-print
In addition, we discuss and improve the performance and utility of the maximum clique finder itself.  ...  We show inter-relationships between maximum cliques and several other common network properties, including network density, maximum core, and number of triangles.  ...  The Heuristic In its search for a maximum clique in the entire graph, the exact algorithm described explores for every vertex v feasible cliques along a subset of the edges incident on v.  ... 
arXiv:1210.5802v2 fatcat:7a7akqlrdzf4bemzpkpo64lvsa

Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage [article]

Ryan A. Rossi, David F. Gleich, Assefaw H. Gebremedhin, Md. Mostofa Ali Patwary
2013 arXiv   pre-print
We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks.  ...  During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search  ...  Consequently, we expect our maximum clique algorithms to be useful for tasks such as analyzing large networks, evaluation of graph generators, community detection, and anomaly detection.  ... 
arXiv:1302.6256v2 fatcat:chorccabwzdddo6wvi3xrvbwx4

Fast Triangle Core Decomposition for Mining Large Graphs [chapter]

Ryan A. Rossi
2014 Lecture Notes in Computer Science  
This paper presents a fast algorithm for computing the triangle core decomposition on big graphs.  ...  Large triangle cores represent dense subgraphs for which each edge has at least k − 2 triangles (same as cliques).  ...  We find that in many cases, the maximum triangle core number gives the exact maximum clique in G, especially for large sparse graphs.  ... 
doi:10.1007/978-3-319-06608-0_26 fatcat:rd6ljbqtzfalde57ywga4c4loe

A Maximum Weight Clique Algorithm For Dense Circle Graphs With Many Shared Endpoints

Max Ward, Andrew Gozzard, Amitava Datta
2017 Journal of Graph Algorithms and Applications  
State-of-the-art algorithms for finding the maximum weight clique of a circle graph are very efficient when the graph is sparse.  ...  However, these algorithms require Θ(n 2 ) time when the graph is dense. We present an algorithm that is a factor of √ n faster for dense graphs in which many chord endpoints are shared.  ...  Acknowledgments The authors wish to thank Eliot Courtney, Zachary Forman, and Connie Pyromallis for their valuable advice and proof reading acumen.  ... 
doi:10.7155/jgaa.00428 fatcat:mezy4r3vwzds7o5tin7fnwcprq

Fast Algorithm for Finding Maximum Clique in Scale-Free Networks

Andrej Jursa
2016 Conference on Theory and Practice of Information Technologies  
Our algorithm is able to solve maximum clique problem for arbitrary graphs, but together with these and some other, less significant pruning techniques, the overall algorithm performs exceptionally well  ...  The maximum clique problem in graph theory concerns finding the largest subset of vertices in which all vertices are connected with an edge.  ...  Algorithm 4 Algorithm for finding maximum clique in scale-free networks. Input: Simple undirected graph G.  ... 
dblp:conf/itat/Jursa16 fatcat:7sxl33qznfawfghyyv7jan2xfu

ahgamut/cliquematch: cliquematch [article]

Gautham
2020 Zenodo  
cliquematch Finding correspondence via maximum cliques in large graphs The cliquematch package aims to do two specific things: Find maximum cliques in large sparse undirected graphs, as quickly and efficiently  ...  to construct large sparse undirected graphs in-memory for such applications.  ...  “A new exact maximum clique algorithm for large and massive sparse graphs”. In: Computers & Operations Research 66, pp. 81– 94.  ... 
doi:10.5281/zenodo.4277288 fatcat:p4ivjl2x3va2jfrh7ztckytt5q

Instantly decodable network coding for real-time device-to-device communications

Ahmed Douik, Sameh Sorour, Tareq Y. Al-Naffouri, Mohamed-Slim Alouini
2016 EURASIP Journal on Advances in Signal Processing  
Due to the complexity of discovering such maximum clique, the paper presents a fast selection algorithm.  ...  With delay minimization problems in IDNC-based systems being equivalent to a maximum weight clique problems in the IDNC graph, the presented algorithms, in this paper, can be applied to different delay  ...  The maximum weight clique in the reduced graph produced by Algorithm 4 is equivalent to the maximum weight clique in the local IDNC graph. Proof.  ... 
doi:10.1186/s13634-015-0293-z fatcat:xoqmm7sfdnhmvct7cjxkwgycfq

Speeding up MCS Algorithm for the Maximum Clique Problem with ILS Heuristic and Other Enhancements [chapter]

Evgeny Maslov, Mikhail Batsyn, Panos M. Pardalos
2013 Springer Proceedings in Mathematics & Statistics  
In this chapter, we present our enhancements of one of the most efficient exact algorithms for the maximum clique problem-MCS algorithm by Tomita, Sutani, Higashi, Takahashi and Wakatsuki (in Proceedings  ...  Our computational experiments show that for dense graphs with a moderate number of vertices (like the majority of DIMACS graphs) it is more efficient to store vertices of a set of candidates and their  ...  Acknowledgements The authors would like to thank professor Mauricio Resende and his coauthors for the source code of their powerful ILS heuristic.  ... 
doi:10.1007/978-1-4614-8588-9_7 fatcat:3yodfxlsgnfz5d7wfynn7wonqa

Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection

Bharath Pattabiraman, Md. Mostofa Ali Patwary, Assefaw H. Gebremedhin, Wei-keng Liao, Alok Choudhary
2015 Internet Mathematics  
We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly.  ...  There exist several algorithms for the problem with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs.  ...  Output: Size of maximum clique. 1: procedure MAXCLIQUE(G = (V, E), lb) 2: Algorithm 2: Heuristic for finding the maximum clique in a graph. Input: Graph G = (V, E).  ... 
doi:10.1080/15427951.2014.986778 fatcat:wvwcxxvgjveh5l3hb7xnxq6q6q
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