Two-phase heuristics for the k-club problem
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | |
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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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 |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799134149381980160 |