CliSAT: A new exact algorithm for hard maximum clique problems

Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial o...

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Detalles Bibliográficos
Autores: San Segundo, Pablo, Furini, Fabio, Álvarez, David, Pardalos, Panos M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/333850
Acceso en línea:http://hdl.handle.net/10261/333850
Access Level:acceso abierto
Palabra clave:Branch -and -bound algorithm
Maximum clique problem
Combinatorial optimization
Exact algorithms
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spelling CliSAT: A new exact algorithm for hard maximum clique problemsSan Segundo, PabloFurini, FabioÁlvarez, DavidPardalos, Panos M.Branch -and -bound algorithmMaximum clique problemCombinatorial optimizationExact algorithmsGiven a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a wide range of applications. The newly developed exact approach is a combinatorial branch-and-bound algorithm that exploits the state-of-the-art branching scheme enhanced by two new bounding techniques with the goal of reducing the branching tree. The first one is based on graph colouring procedures and partial maximum satisfiability problems arising in the branching scheme. The second one is a filtering phase based on constraint programming and domain propagation techniques. CliSAT is designed for structured MCP instances which are computationally difficult to solve since they are dense and contain many interconnected large cliques. Extensive experiments on hard benchmark instances, as well as new hard instances arising from different applications, show that CliSAT outperforms the state-of-the-art MCP algorithms, in some cases by several orders of magnitude.This publication is part of the R&D project “Cognitive Personal Assistance for Social Environments (ACOGES)”, reference PID2020-113096RB-I00, funded by MCIN/AEI/10.13039/501100011033.Peer reviewedElsevierMinisterio de Ciencia e Innovación (España)San Segundo, Pablo [0000-0001-7050-5563]Furini, Fabio [0000-0002-1839-5827]Álvarez, David [0000-0002-2190-7950]Pardalos, Panos M. [0000-0001-9623-8053]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202320232023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/333850reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113096RB-I00https://doi.org/10.1016/j.ejor.2022.10.028Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3338502026-05-22T06:33:51Z
dc.title.none.fl_str_mv CliSAT: A new exact algorithm for hard maximum clique problems
title CliSAT: A new exact algorithm for hard maximum clique problems
spellingShingle CliSAT: A new exact algorithm for hard maximum clique problems
San Segundo, Pablo
Branch -and -bound algorithm
Maximum clique problem
Combinatorial optimization
Exact algorithms
title_short CliSAT: A new exact algorithm for hard maximum clique problems
title_full CliSAT: A new exact algorithm for hard maximum clique problems
title_fullStr CliSAT: A new exact algorithm for hard maximum clique problems
title_full_unstemmed CliSAT: A new exact algorithm for hard maximum clique problems
title_sort CliSAT: A new exact algorithm for hard maximum clique problems
dc.creator.none.fl_str_mv San Segundo, Pablo
Furini, Fabio
Álvarez, David
Pardalos, Panos M.
author San Segundo, Pablo
author_facet San Segundo, Pablo
Furini, Fabio
Álvarez, David
Pardalos, Panos M.
author_role author
author2 Furini, Fabio
Álvarez, David
Pardalos, Panos M.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
San Segundo, Pablo [0000-0001-7050-5563]
Furini, Fabio [0000-0002-1839-5827]
Álvarez, David [0000-0002-2190-7950]
Pardalos, Panos M. [0000-0001-9623-8053]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Branch -and -bound algorithm
Maximum clique problem
Combinatorial optimization
Exact algorithms
topic Branch -and -bound algorithm
Maximum clique problem
Combinatorial optimization
Exact algorithms
description Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a wide range of applications. The newly developed exact approach is a combinatorial branch-and-bound algorithm that exploits the state-of-the-art branching scheme enhanced by two new bounding techniques with the goal of reducing the branching tree. The first one is based on graph colouring procedures and partial maximum satisfiability problems arising in the branching scheme. The second one is a filtering phase based on constraint programming and domain propagation techniques. CliSAT is designed for structured MCP instances which are computationally difficult to solve since they are dense and contain many interconnected large cliques. Extensive experiments on hard benchmark instances, as well as new hard instances arising from different applications, show that CliSAT outperforms the state-of-the-art MCP algorithms, in some cases by several orders of magnitude.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/333850
url http://hdl.handle.net/10261/333850
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113096RB-I00
https://doi.org/10.1016/j.ejor.2022.10.028
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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