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Fast maximum clique algorithms for large graphs

2014
*
Proceedings of the 23rd International Conference on World Wide Web - WWW '14 Companion
*

We propose a

doi:10.1145/2567948.2577283
dblp:conf/www/RossiGGP14
fatcat:euicae4rqzcapbjzxvaxwencke
*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*. ...##
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Parallel Maximum Clique Algorithms with Applications to Network Analysis

2015
*
SIAM Journal on Scientific Computing
*

We propose a

doi:10.1137/14100018x
fatcat:6enika5twfgl7ccu2jbwumzemm
*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. ...##
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A Fast Heuristic Algorithm Based on Verification and Elimination Methods for Maximum Clique Problem
[article]

2007
*
arXiv
*
pre-print

We have succeeded in developing a

arXiv:0710.0748v1
fatcat:pore6jioenhilb6i5l2b7mdp4i
*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. ...##
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Approximate Maximum Clique Algorithm (AMCA): A Clever Technique for Solving the Maximum Clique Problem through Near Optimal Algorithm for Minimum Vertex Cover Problem

2018
*
International Journal of Control and Automation
*

The only way left is to use the approximation

doi:10.14257/ijca.2018.11.3.04
fatcat:irnddjzbrngolmdert2qiamfrm
*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*. ...##
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Solving large Maximum Clique problems on a quantum annealer
[article]

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*. ...

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

2012
*
arXiv
*
pre-print

We present a new exact

arXiv:1209.5818v4
fatcat:67sqkj5h7rf6bfjzn7xpgiai2a
*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). ...##
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What if CLIQUE were fast? Maximum Cliques in Information Networks and Strong Components in Temporal Networks
[article]

2012
*
arXiv
*
pre-print

In addition, we discuss and improve the performance and utility of the

arXiv:1210.5802v2
fatcat:7a7akqlrdzf4bemzpkpo64lvsa
*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. ...##
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Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage
[article]

2013
*
arXiv
*
pre-print

We propose a

arXiv:1302.6256v2
fatcat:chorccabwzdddo6wvi3xrvbwx4
*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. ...##
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Fast Triangle Core Decomposition for Mining Large Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

This paper presents a

doi:10.1007/978-3-319-06608-0_26
fatcat:rd6ljbqtzfalde57ywga4c4loe
*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*. ...##
###
A Maximum Weight Clique Algorithm For Dense Circle Graphs With Many Shared Endpoints

2017
*
Journal of Graph Algorithms and Applications
*

State-of-the-art

doi:10.7155/jgaa.00428
fatcat:mezy4r3vwzds7o5tin7fnwcprq
*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. ...##
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Fast Algorithm for Finding Maximum Clique in Scale-Free Networks

2016
*
Conference on Theory and Practice of Information Technologies
*

Our

dblp:conf/itat/Jursa16
fatcat:7sxl33qznfawfghyyv7jan2xfu
*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. ...##
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ahgamut/cliquematch: cliquematch
[article]

2020
*
Zenodo
*

cliquematch Finding correspondence via

doi:10.5281/zenodo.4277288
fatcat:p4ivjl2x3va2jfrh7ztckytt5q
*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. ...##
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Instantly decodable network coding for real-time device-to-device communications

2016
*
EURASIP Journal on Advances in Signal Processing
*

Due to the complexity of discovering such

doi:10.1186/s13634-015-0293-z
fatcat:xoqmm7sfdnhmvct7cjxkwgycfq
*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. ...##
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Speeding up MCS Algorithm for the Maximum Clique Problem with ILS Heuristic and Other Enhancements
[chapter]

2013
*
Springer Proceedings in Mathematics & Statistics
*

In this chapter, we present our enhancements of one of the most efficient exact

doi:10.1007/978-1-4614-8588-9_7
fatcat:3yodfxlsgnfz5d7wfynn7wonqa
*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. ...##
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Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection

2015
*
Internet Mathematics
*

We present a new exact

doi:10.1080/15427951.2014.986778
fatcat:wvwcxxvgjveh5l3hb7xnxq6q6q
*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). ...
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