Fast local search for the maximum independent set problem

Andrade, Diogo V.; Resende, Maurício G. C.; Werneck, Renato F.

doi:10.1007/s10732-012-9196-4

Cited by 120 publications

(96 citation statements)

References 16 publications

(24 reference statements)

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“…The new MCS that was composed of a combination of the KLS procedure and MCS in Ref. [32] as above was named MCS 1 .…”

Section: An Approximate Solution As An Initial Lower Boundmentioning

confidence: 99%

“…ILS&MCS [17] and BG14 [2] require more time than k5 MCT for most of the instances tested. One reason for this difference comes from the fact that our approximation algorithm, KLS, takes up only small portion of the total algorithm's computing time with c 2017 Information Processing Society of Japan few exceptions, whereas their approximation algorithm, ILS [1] in ILS&MCS and BG14, consumes a considerable part of the total computing time.…”

Section: Overall Improvementmentioning

confidence: 99%

“…In this paper, we present improvements to MCS to make it 1 The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan wakatsuki.mitsuo@uec.ac.jp much faster. First, we turn back to our original MCS [25] that employs an approximation algorithm for the maximum clique problem at the beginning in order to obtain an initial lower bound on the size of a maximum clique, as noted at Concluding Remarks in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[35] with a slight modification. (1) We are concerned with a simple undirected graph G = (V, E) with a finite set V of vertices and a finite set E of edges that comprise unordered pairs (v, w) (= (w, v)) of distinct vertices. The set V of vertices is considered to be ordered, and the i-th element in V is denoted by V [i].…”

Section: Introductionmentioning

confidence: 99%

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A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments

Tomita

Matsuzaki

Nagao

et al. 2017

Journal of Information Processing

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Abstract:We present further improvements to a branch-and-bound maximum-clique-finding algorithm MCS (WALCOM 2010, LNCS 5942, pp.191-203) that was shown to be fast. First, we employ a variant of an efficient approximation algorithm KLS for finding a maximum clique. Second, we make use of appropriate sorting of vertices only near the root of the search tree. Third, we employ a lightened approximate coloring mainly near the leaves of the search tree. A new algorithm obtained from MCS with the above improvements is named k5 MCT. It is shown that k5 MCT is much faster than MCS by extensive computational experiments. In particular, k5 MCT is shown to be faster than MCS for gen400 p0.9 75, gen400 p0.9 65 and gen400 p0.9 55 by over 81,000, 39,000 and 19,000 times, respectively.

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“…The new MCS that was composed of a combination of the KLS procedure and MCS in Ref. [32] as above was named MCS 1 .…”

Section: An Approximate Solution As An Initial Lower Boundmentioning

confidence: 99%

Section: Overall Improvementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments

Tomita

Matsuzaki

Nagao

et al. 2017

Journal of Information Processing

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“…It is easy to see that the complement of an independent set I is a vertex cover V \I and an independent set in G is a clique in the complement graph G. Since all of these problems are NP-hard [17], heuristic algorithms are used in practice to efficiently compute solutions of high quality on large graphs [2,21]. However, small graphs with hundreds to thousands of vertices may often be solved in practice with traditional branch-and-bound methods [34,35,41], and mediumsized instances can be solved exactly in practice using reduction rules to kernelize the graph.…”

Section: Introductionmentioning

confidence: 99%

Finding Near-Optimal Independent Sets at Scale

Lamm¹,

Sanders²,

Schulz³

et al. 2015

2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs, which typically take exponential time to solve exactly using the best-known exact algorithms. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space-which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.

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Approaches for finding cohesive subgroups in large‐scale social networks via maximum k‐plex detection

Miao

Balasundaram

2017

Networks

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A k‐plex is a clique relaxation introduced in social network analysis to model cohesive social subgroups that allows for a limited number of nonadjacent vertices (strangers) inside the cohesive subgroup. Several exact algorithms and heuristic approaches to find a maximum‐size k‐plex in the graph have been developed recently for this NP‐hard problem. This article develops a greedy randomized adaptive search procedure (GRASP) for the maximum k‐plex problem. We offer a key improvement in the design of the construction procedure that alleviates a drawback observed in multiple past studies. In existing construction heuristics, k‐plexes found for smaller values of parameter k are sometimes not found for larger k even though they are feasible; instead inferior solutions are found. We identify the reasons behind this behavior and address these in our new construction procedure. We then show that an existing exact algorithm for solving this problem on power‐law graphs can be considerably enhanced by using GRASP. The overall approach is able to solve the problem to optimality on massive social networks, including some with several million vertices and edges. These are orders of magnitude larger than the largest real‐life social networks on which this problem has been solved to optimality in the current literature. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 69(4), 388–407 2017

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Fast local search for the maximum independent set problem

Cited by 120 publications

References 16 publications

A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments

A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments

Finding Near-Optimal Independent Sets at Scale

Approaches for finding cohesive subgroups in large‐scale social networks via maximum k‐plex detection

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