Publicação
An analytical comparison of the LP relaxations of integer models for the k-club problem
| Resumo: | Given an undirected graph G = (V,E), a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem is to find a maximum cardinality k-club. In this study, we use a linear programming relaxation standpoint to compare integer formulations for the k-club problem. The comparisons involve formulations known from the literature and new formulations, built in different variable spaces. For the case k = 3, we propose two enhanced compact formulations. From the LP relaxation standpoint these formulations dominate all other compact formulations in the literature and are equivalent to a formulation with a non-polynomial number of constraints. Also for k = 3, we compare the relative strength of LP relaxations for all formulations examined in the study (new and known from the literature). Based on insights obtained from the comparative study, we devise a strengthened version of a recursive compact formulation in the literature for the k-club problem (k > 1) and show how to modify one of the new formulations for the case k = 3 in order to accommodate additional constraints recently proposed in the literature. |
|---|---|
| Autores principais: | Almeida, Maria Teresa |
| Outros Autores: | Carvalho, Filipa D. |
| Assunto: | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| Ano: | 2014 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| _version_ | 1866811501684195328 |
|---|---|
| author | Almeida, Maria Teresa |
| author2 | Carvalho, Filipa D. |
| author2_role | author |
| author_facet | Almeida, Maria Teresa Carvalho, Filipa D. |
| author_role | author |
| contributor_name_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Almeida, Maria Teresa\"},{\"Person.name\":\"Carvalho, Filipa D.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| datacite.creators.creator.creatorName.fl_str_mv | Almeida, Maria Teresa Carvalho, Filipa D. |
| datacite.date.Accepted.fl_str_mv | 2014-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2023-10-30T14:39:45Z |
| datacite.date.embargoed.fl_str_mv | 2023-10-30T14:39:45Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| datacite.titles.title.fl_str_mv | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| dc.contributor.none.fl_str_mv | Repositório Científico de Acesso Aberto da ULisboa |
| dc.creator.none.fl_str_mv | Almeida, Maria Teresa Carvalho, Filipa D. |
| dc.date.Accepted.fl_str_mv | 2014-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2023-10-30T14:39:45Z |
| dc.date.embargoed.fl_str_mv | 2023-10-30T14:39:45Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.5/29153 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| dc.title.fl_str_mv | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | Given an undirected graph G = (V,E), a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem is to find a maximum cardinality k-club. In this study, we use a linear programming relaxation standpoint to compare integer formulations for the k-club problem. The comparisons involve formulations known from the literature and new formulations, built in different variable spaces. For the case k = 3, we propose two enhanced compact formulations. From the LP relaxation standpoint these formulations dominate all other compact formulations in the literature and are equivalent to a formulation with a non-polynomial number of constraints. Also for k = 3, we compare the relative strength of LP relaxations for all formulations examined in the study (new and known from the literature). Based on insights obtained from the comparative study, we devise a strengthened version of a recursive compact formulation in the literature for the k-club problem (k > 1) and show how to modify one of the new formulations for the case k = 3 in order to accommodate additional constraints recently proposed in the literature. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorio.ulisboa.pt/bitstreams/cf26c89e-08ef-49ba-8c0d-a98440dcf952/download |
| id | ul_85cc75dab0cdcbbdfd1aa021122c145b |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.5/29153 |
| instacron_str | ul |
| institution | Universidade de Lisboa |
| instname_str | Universidade de Lisboa |
| language | eng |
| network_acronym_str | ul |
| network_name_str | Repositório da Universidade de Lisboa |
| oai_identifier_str | oai:repositorio.ulisboa.pt:10400.5/29153 |
| organization_str_mv | urn:organizationAcronym:ul |
| person_str_mv | Almeida, Maria Teresa Carvalho, Filipa D. |
| publishDate | 2014 |
| publisher.none.fl_str_mv | Elsevier |
| reponame_str | Repositório da Universidade de Lisboa |
| repository_id_str | urn:repositoryAcronym:ul |
| service_str_mv | urn:repositoryAcronym:ul |
| spelling | engElsevierpt_PTGiven an undirected graph G = (V,E), a k-club is a subset of nodes that induces a subgraph with diameter at most k. The k-club problem is to find a maximum cardinality k-club. In this study, we use a linear programming relaxation standpoint to compare integer formulations for the k-club problem. The comparisons involve formulations known from the literature and new formulations, built in different variable spaces. For the case k = 3, we propose two enhanced compact formulations. From the LP relaxation standpoint these formulations dominate all other compact formulations in the literature and are equivalent to a formulation with a non-polynomial number of constraints. Also for k = 3, we compare the relative strength of LP relaxations for all formulations examined in the study (new and known from the literature). Based on insights obtained from the comparative study, we devise a strengthened version of a recursive compact formulation in the literature for the k-club problem (k > 1) and show how to modify one of the new formulations for the case k = 3 in order to accommodate additional constraints recently proposed in the literature.application/pdfpt_PTAn analytical comparison of the LP relaxations of integer models for the k-club problemAlmeida, Maria TeresaCarvalho, Filipa D.HostingInstitutionOrganizationalRepositório Científico de Acesso Aberto da ULisboae-mailmailto:repositorio@reitoria.ulisboa.ptrepositorio@reitoria.ulisboa.ptISSNIsPartOf0377-2217DOIIsPartOfdoi.org/10.1016/j.ejor.2013.08.0042023-10-30T14:39:45Z20142014-01-01T00:00:00ZHandlehttp://hdl.handle.net/10400.5/29153http://purl.org/coar/access_right/c_abf2open accessCombinatorial OptimizationFormulationsK-ClubsInteger ProgrammingClique Relaxations580362 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorio.ulisboa.pt/bitstreams/cf26c89e-08ef-49ba-8c0d-a98440dcf952/download |
| spellingShingle | An analytical comparison of the LP relaxations of integer models for the k-club problem Almeida, Maria Teresa Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| status | SINGLETON |
| subject.fl_str_mv | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| title | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| title_full | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| title_fullStr | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| title_full_unstemmed | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| title_short | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| title_sort | An analytical comparison of the LP relaxations of integer models for the k-club problem |
| topic | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| topic_facet | Combinatorial Optimization Formulations K-Clubs Integer Programming Clique Relaxations |
| url | http://hdl.handle.net/10400.5/29153 |
| visible | 1 |