Combining Graph Structure Exploitation and Propositional Reasoning for the Maximum Clique Problem

Li, Chu-Min; Quan, Zhe

doi:10.1109/ictai.2010.57

Cited by 28 publications

(30 citation statements)

References 11 publications

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“…From Ref. [22], Tables 3-4 also include the calibrated computing time of MaxCLQ [14], [15] by Li and Quan that is based on MaxSAT. The calibrated computing time by ILS&MCS [17] and BG14 [2] are added on the assumption that the performance of each MCS is the same as that in this paper, for reference, too.…”

Section: Stepwise Improvementmentioning

confidence: 99%

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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Section: Stepwise Improvementmentioning

confidence: 99%

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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“…Konc and Janezic (2007), Tomita and Kameda (2007), Li and Quan (2010b) apply the greedy strategy proposed by Tomita and Seki (2003) to partition the graph into independent sets, and use the number of independent sets in the partition as an upper bound for MC. MaxCLQ (Li & Quan, 2010b, 2010a encodes an MC instance into a partial MaxSAT instance and improves the upper bound based on the independent set partition by making use of MaxSAT reasoning. The excellent performance of Max-CLQ shows that MaxSAT reasoning technologies allows to compute a tight upper bound for MC within reasonable time.…”

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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“…Fahle [8] and Régin [9] use a constraint-based approach to prune the search space, but the majority of current efficient solvers are color-based, i.e. they employ a greedy coloring heuristic to compute an upper bound for the clique number of every subproblem, as in [10][11][12][13][14][15][16][17][18][19]. Interesting recent comparison surveys for exact maximum clique algorithms have been reported by Prosser [20] and Wu & Hao's [24].…”

Section: Introductionmentioning

confidence: 99%

“…Interesting recent comparison surveys for exact maximum clique algorithms have been reported by Prosser [20] and Wu & Hao's [24]. They show MCS [15], MaxCLQ [18], and bit optimized BBMC [12][13] as the current fastest algorithms at present.…”

Section: Introductionmentioning

confidence: 99%

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Infra-chromatic bound for exact maximum clique search

Segundo

Nikolaev

Batsyn

2015

Computers & Operations Research

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Combining Graph Structure Exploitation and Propositional Reasoning for the Maximum Clique Problem

Cited by 28 publications

References 11 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

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

Infra-chromatic bound for exact maximum clique search

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