Relaxed approximate coloring in exact maximum clique search

Segundo, Pablo San; Tapia, Cristóbal

doi:10.1016/j.cor.2013.10.018

Cited by 39 publications

(32 citation statements)

References 11 publications

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“…In this section we provide some results of computational experiments conducted in order to explore whether the proposed method is useful as a cut-generating tool for the MSS problem. Our main goal is not to provide a competitive algorithm for the MSS problem, since combinatorial algorithms are much more effective than cutting-plane algorithms for this problem [7,19]. As already pointed out in [17], the facts that other combinatorial problems may be formulated including stable set constraints, either explicitly or devised to address their vertex packing relaxation, are motivations to the investigation of efficient polyhedral methods for the stable set problem.…”

Section: Computational Experiments and Analysis Of Resultsmentioning

confidence: 99%

General cut-generating procedures for the stable set polytope

Corrêa

Donne

Koch

et al. 2018

Discrete Applied Mathematics

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We propose general separation procedures for generating cuts for the stable set polytope, inspired by a procedure by Rossi and Smriglio and applying a lifting method by Xavier and Campêlo. In contrast to existing cut-generating procedures, ours generate both rank and non-rank valid inequalities, hence they are of a more general nature than existing methods. This is accomplished by iteratively solving a lifting problem, which consists of a maximum weighted stable set problem on a smaller graph. Computational experience on DIMACS benchmark instances shows that the proposed approach may be a useful tool for generating cuts for the stable set polytope. 1 This work has been partially supported by the Stic/AmSud joint program by CAPES (Brazil), CNRS and MAE (France), CONICYT (Chile) and MINCYT (Argentina) -project 13STIC-05-and the Pronem program by FUNCAP/CNPq (Brazil) -project ParGO.

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Section: Computational Experiments and Analysis Of Resultsmentioning

confidence: 99%

General cut-generating procedures for the stable set polytope

Corrêa

Donne

Koch

et al. 2018

Discrete Applied Mathematics

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“…This is a reasonable assumption because, as mentioned in the introductory section, the more recent algorithms, such as improved variants of BBMC [15] or IncMaxCLQ [16], are not expected to work well over the networks of interest to this paper. FMC has been designed for massive sparse graphs but, as will be shown, performs very poorly in the reported set, so it is enough to establish PMC as the better algorithm and the reason why we have not considered necessary to add more results of FMC in this report.…”

Section: Comparison With Other Algorithmsmentioning

confidence: 99%

“…Only very recently a number of improvements have appeared connected with more sophisticated approximate coloring techniques: BBMCL [15] improves BBMC using a selective coloring scheme and IncMaxCLQ [16] encodes each colored subproblem to MaxSAT and uses logical inferences to find subsets of vertices assigned k colors which cannot possibly make part of a k-clique (referred to as inconsistent subsets). In a similar vein is a variant of BBMC denoted as infra-chromatic which searches for a simpler form of inconsistent subsets without resorting to logical reasoning [18].…”

Section: Introductionmentioning

confidence: 99%

A new exact maximum clique algorithm for large and massive sparse graphs

Segundo

Lopez

Pardalos

2016

Computers & Operations Research

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“…and possibly with shortcuts taken for certain vertices [48], and possibly followed by a repair step to improve the colouring [53], or stronger bounding rules based upon MaxSAT inference [25,26,46]). Such colourings will not give us the required property that vertices in remaining ∩ connected come last (so they are selected first by the reverse branching order).…”

Section: Ensuring Connectedness In a Clique-based Approachmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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Relaxed approximate coloring in exact maximum clique search

Cited by 39 publications

References 11 publications

General cut-generating procedures for the stable set polytope

General cut-generating procedures for the stable set polytope

A new exact maximum clique algorithm for large and massive sparse graphs

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

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