Multi-neighborhood tabu search for the maximum weight clique problem

Wu, Qinghua; Hao, Jin‐Kao; Glover, Fred

doi:10.1007/s10479-012-1124-3

Cited by 89 publications

(83 citation statements)

References 25 publications

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“…Other approaches The problem has also been tackled using mathematical programming [25,27,61], and is the subject of ongoing research for inexact (heuristic) solutions [3,4,10,20,27,29,41,62,65,66]. Finally, sometimes alternative constraints or objectives are considered [6,34,54].…”

Section: Maximum Weight Clique Algorithmsmentioning

confidence: 99%

“…This rule, together with a similar rule for allocating weights to edges for the edge-weighted variant of the problem, is very widely used [2][3][4][20][21][22]25,27,29,32,34,[41][42][43]45,55,61,62,65,66, and many more], often as the only way of evaluating a solver. It has also recently been adopted for large sparse graphs [10,20,29,62], and for benchmarking the minimum weight dominating set problem [63].…”

Section: Current Practices In Benchmarkingmentioning

confidence: 99%

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On Maximum Weight Clique Algorithms, and How They Are Evaluated

McCreesh

Prosser

Simpson

et al. 2017

Lecture Notes in Computer Science

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Abstract. Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algorithms, and that additionally, weight distributions affect whether certain inference rules are cost-effective. We look at other families of benchmark instances for the maximum weight clique problem, coming from winner determination problems, graph colouring, and error-correcting codes, and introduce two new families of instances, based upon kidney exchange and the Research Excellence Framework. In each case the weights carry much more interesting structure, and do not in any way resemble the 200 rule. We make these instances available in the hopes of improving the quality of future experiments.

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Section: Maximum Weight Clique Algorithmsmentioning

confidence: 99%

Section: Current Practices In Benchmarkingmentioning

confidence: 99%

On Maximum Weight Clique Algorithms, and How They Are Evaluated

McCreesh

Prosser

Simpson

et al. 2017

Lecture Notes in Computer Science

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“…The weight of a clique C in G is defined to be w(C) = v∈C w(v). Given a weighted graph G, the maximum weight clique problem asks to find a clique with the largest weight in G (Östergård, 2001;Pullan, 2008;Wu et al, 2012) and this largest weight is often denoted by ω v (G) in the literature. Note that a maximum weight clique is not necessarily a clique containing the maximum number of vertices, but it must be a maximal clique.…”

Section: Preliminariesmentioning

confidence: 99%

“…MinSatz constructs a weighted graph for the MinSAT instance and uses the clique partition combined with MaxSAT reasoning to compute a tight bound for the MinSAT instance to solve. In addition to exact algorithms, some heuristic algorithms are also proposed to solve the MWC problem (Pullan, 2008;Wu, Hao, & Glover, 2012;Benlic & Hao, 2013).…”

Section: Introductionmentioning

confidence: 99%

An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Fang¹,

Li²,

Xu³

2016

jair

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Recently, MaxSAT reasoning is shown very effective in computing a tight upper bound for a Maximum Clique (MC) of a (unweighted) graph. In this paper, we apply MaxSAT reasoning to compute a tight upper bound for a Maximum Weight Clique (MWC) of a wighted graph. We first study three usual encodings of MWC into weighted partial MaxSAT dealing with hard clauses, which must be satisfied in all solutions, and soft clauses, which are weighted and can be falsified. The drawbacks of these encodings motivate us to propose an encoding of MWC into a special weighted partial MaxSAT formalism, called LW (Literal-Weighted) encoding and dedicated for upper bounding an MWC, in which both soft clauses and literals in soft clauses are weighted. An optimal solution of the LW MaxSAT instance gives an upper bound for an MWC, instead of an optimal solution for MWC. We then introduce two notions called the Top-k literal failed clause and the Top-k empty clause to extend classical MaxSAT reasoning techniques, as well as two sound transformation rules to transform an LW MaxSAT instance. Successive transformations of an LW MaxSAT instance driven by MaxSAT reasoning give a tight upper bound for the encoded MWC. The approach is implemented in a branch-and-bound algorithm called MWCLQ. Experimental evaluations on the broadly used DIMACS benchmark, BHOSLIB benchmark, random graphs and the benchmark from the winner determination problem show that our approach allows MWCLQ to reduce the search space significantly and to solve MWC instances effectively. Consequently, MWCLQ outperforms state-of-the-art exact algorithms on the vast majority of instances. Moreover, it is surprisingly effective in solving hard and dense instances.

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“…Let G=(V,E) be an undirected graph with vertex set V={1, 2, …, n} and edge set E⊆V×V, A clique [1][2][3][4] of G is the set of vertices C⊆V, such that i,j∈E for all i,j∈C. A maximum clique is a clique with maximum cardinality among all cliques of G. Due to its numerous applications, the maximum clique problem is one of the most important NPhard problems [5] and it has been extensively studied in the literature such as clustering in social networks [6][7].…”

Section: Introductionmentioning

confidence: 99%

Solving maximum clique problem in stochastic graphs using learning automata

Soleimani-Pouri

Rezvanian

Meybodi

2012

2012 Fourth International Conference on Computational Aspects of Social Networks (CASoN)

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Abstract-The maximum clique of a given graph G is the subgraph C of G such that two vertices in C are adjacent in G with maximum cardinality. Finding the maximum clique in an arbitrary graph is an NP-Hard problem, motivated by the social networks analysis. In the real world applications, the nature of interaction between nodes is stochastic and the probability distribution function of the vertex weight is unknown. In this paper a learning automata-based algorithm is proposed for solving maximum clique problem in the stochastic graph. The simulation results on stochastic graph demonstrate that the proposed algorithm outperforms standard sampling method in terms of the number of samplings taken by algorithm.

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Multi-neighborhood tabu search for the maximum weight clique problem

Cited by 89 publications

References 25 publications

On Maximum Weight Clique Algorithms, and How They Are Evaluated

On Maximum Weight Clique Algorithms, and How They Are Evaluated

An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Solving maximum clique problem in stochastic graphs using learning automata

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