Two-phase heuristics for the k-club problem

Detalhes bibliográficos
Autor(a) principal: Almeida, Maria Teresa
Data de Publicação: 2014
Outros Autores: Carvalho, Filipa D.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.5/29152
Resumo: Given an undirected graph G and an integer k, a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem consists of identifying a maximum cardinality k-club in G. It is an NP-hard problem. The problem of checking if a given k-club is maximal or if it is a subset of a larger k-club is also NP-hard, due to the non-hereditary nature of the k-club structure. This non-hereditary nature is adverse for heuristic strategies that rely on single-element add and delete operations. In this work we propose two-phase algorithms which combine simple construction schemes with exact optimization of restricted integer models to generate near optimal solutions for the k-club problem. Numerical experiments on sets of uniform random graphs with edge densities known to be very challenging and test instances available in the literature indicate that the new algorithms are quite effective, both in terms of solution quality and running times.
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spelling Two-phase heuristics for the k-club problemHeuristicsMaximum K-ClubClique RelaxationsSocial Network AnalysisComputational BiologyGiven an undirected graph G and an integer k, a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem consists of identifying a maximum cardinality k-club in G. It is an NP-hard problem. The problem of checking if a given k-club is maximal or if it is a subset of a larger k-club is also NP-hard, due to the non-hereditary nature of the k-club structure. This non-hereditary nature is adverse for heuristic strategies that rely on single-element add and delete operations. In this work we propose two-phase algorithms which combine simple construction schemes with exact optimization of restricted integer models to generate near optimal solutions for the k-club problem. Numerical experiments on sets of uniform random graphs with edge densities known to be very challenging and test instances available in the literature indicate that the new algorithms are quite effective, both in terms of solution quality and running times.ElsevierRepositório da Universidade de LisboaAlmeida, Maria TeresaCarvalho, Filipa D.2023-10-30T14:07:37Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29152engAlmeida, Maria Teresa and Filipa D. Carvalho .(2014). “Two-phase heuristics for the k-club problem”. Computers & Operations Research, Volume 52, Part A: pp 94-104. (Search PDF in 2023).0305-0548doi.org/10.1016/j.cor.2014.07.006info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-05T01:31:47Zoai:www.repository.utl.pt:10400.5/29152Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:26:46.527537Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Two-phase heuristics for the k-club problem
title Two-phase heuristics for the k-club problem
spellingShingle Two-phase heuristics for the k-club problem
Almeida, Maria Teresa
Heuristics
Maximum K-Club
Clique Relaxations
Social Network Analysis
Computational Biology
title_short Two-phase heuristics for the k-club problem
title_full Two-phase heuristics for the k-club problem
title_fullStr Two-phase heuristics for the k-club problem
title_full_unstemmed Two-phase heuristics for the k-club problem
title_sort Two-phase heuristics for the k-club problem
author Almeida, Maria Teresa
author_facet Almeida, Maria Teresa
Carvalho, Filipa D.
author_role author
author2 Carvalho, Filipa D.
author2_role author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Almeida, Maria Teresa
Carvalho, Filipa D.
dc.subject.por.fl_str_mv Heuristics
Maximum K-Club
Clique Relaxations
Social Network Analysis
Computational Biology
topic Heuristics
Maximum K-Club
Clique Relaxations
Social Network Analysis
Computational Biology
description Given an undirected graph G and an integer k, a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem consists of identifying a maximum cardinality k-club in G. It is an NP-hard problem. The problem of checking if a given k-club is maximal or if it is a subset of a larger k-club is also NP-hard, due to the non-hereditary nature of the k-club structure. This non-hereditary nature is adverse for heuristic strategies that rely on single-element add and delete operations. In this work we propose two-phase algorithms which combine simple construction schemes with exact optimization of restricted integer models to generate near optimal solutions for the k-club problem. Numerical experiments on sets of uniform random graphs with edge densities known to be very challenging and test instances available in the literature indicate that the new algorithms are quite effective, both in terms of solution quality and running times.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2023-10-30T14:07:37Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/29152
url http://hdl.handle.net/10400.5/29152
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Almeida, Maria Teresa and Filipa D. Carvalho .(2014). “Two-phase heuristics for the k-club problem”. Computers & Operations Research, Volume 52, Part A: pp 94-104. (Search PDF in 2023).
0305-0548
doi.org/10.1016/j.cor.2014.07.006
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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