Integer models and upper bounds for the 3-club problem
Autor(a) principal: | |
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Data de Publicação: | 2012 |
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/10400.5/29166 |
Resumo: | Given an undirected graph, the k -club problem seeks a maximum cardinality subset of nodes that induces a subgraph with diameter at most k . We present two new formulations for the 3-club problem: one is compact and the other has a nonpolynomial number of constraints. By defining an integer compact relaxation of the second formulation, we obtain a new upper bound on the 3-club optimum that improves on the 3-clique number bound. We derive new families of valid inequalities for the 3-club polytope and use them to strengthen the LP relaxations of the new models. The computational study is performed on 120 graphs with up to 200 nodes and edge densities reported in the literature to produce difficult instances of the 3-club problem. The results show that the new compact formulation is competitive with the exact solution methods reported in the literature, and that a large proportion of the LP gap is bridged with the new valid inequalities. |
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Integer models and upper bounds for the 3-club problemDiameter Constrained ProblemsK-ClubInteger FormulationsClique RelaxationsSocial Network AnalysisGiven an undirected graph, the k -club problem seeks a maximum cardinality subset of nodes that induces a subgraph with diameter at most k . We present two new formulations for the 3-club problem: one is compact and the other has a nonpolynomial number of constraints. By defining an integer compact relaxation of the second formulation, we obtain a new upper bound on the 3-club optimum that improves on the 3-clique number bound. We derive new families of valid inequalities for the 3-club polytope and use them to strengthen the LP relaxations of the new models. The computational study is performed on 120 graphs with up to 200 nodes and edge densities reported in the literature to produce difficult instances of the 3-club problem. The results show that the new compact formulation is competitive with the exact solution methods reported in the literature, and that a large proportion of the LP gap is bridged with the new valid inequalities.John Wiley & Sons | Wiley OolineRepositório da Universidade de LisboaAlmeida, Maria TeresaCarvalho, Filipa D.2023-11-02T09:03:07Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/29166engAlmeida, Maria Teresa and Filipa D. Carvalho .(2012). “Integer models and upper bounds for the 3-club problem”. NETWORKS, Vol. 60, No. 3: pp. 155–166 (Search PDF in 2023).DOI 10.1002/netinfo: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:RCAAP2023-11-05T01:31:55Zoai:www.repository.utl.pt:10400.5/29166Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:26:47.901716Repositório 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 |
Integer models and upper bounds for the 3-club problem |
title |
Integer models and upper bounds for the 3-club problem |
spellingShingle |
Integer models and upper bounds for the 3-club problem Almeida, Maria Teresa Diameter Constrained Problems K-Club Integer Formulations Clique Relaxations Social Network Analysis |
title_short |
Integer models and upper bounds for the 3-club problem |
title_full |
Integer models and upper bounds for the 3-club problem |
title_fullStr |
Integer models and upper bounds for the 3-club problem |
title_full_unstemmed |
Integer models and upper bounds for the 3-club problem |
title_sort |
Integer models and upper bounds for the 3-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 |
Diameter Constrained Problems K-Club Integer Formulations Clique Relaxations Social Network Analysis |
topic |
Diameter Constrained Problems K-Club Integer Formulations Clique Relaxations Social Network Analysis |
description |
Given an undirected graph, the k -club problem seeks a maximum cardinality subset of nodes that induces a subgraph with diameter at most k . We present two new formulations for the 3-club problem: one is compact and the other has a nonpolynomial number of constraints. By defining an integer compact relaxation of the second formulation, we obtain a new upper bound on the 3-club optimum that improves on the 3-clique number bound. We derive new families of valid inequalities for the 3-club polytope and use them to strengthen the LP relaxations of the new models. The computational study is performed on 120 graphs with up to 200 nodes and edge densities reported in the literature to produce difficult instances of the 3-club problem. The results show that the new compact formulation is competitive with the exact solution methods reported in the literature, and that a large proportion of the LP gap is bridged with the new valid inequalities. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2012-01-01T00:00:00Z 2023-11-02T09:03:07Z |
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/10400.5/29166 |
url |
http://hdl.handle.net/10400.5/29166 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Almeida, Maria Teresa and Filipa D. Carvalho .(2012). “Integer models and upper bounds for the 3-club problem”. NETWORKS, Vol. 60, No. 3: pp. 155–166 (Search PDF in 2023). DOI 10.1002/net |
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 |
John Wiley & Sons | Wiley Ooline |
publisher.none.fl_str_mv |
John Wiley & Sons | Wiley Ooline |
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 |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
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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1799134149427068928 |