A polyhedral study of the maximum edge subgraph problem

Autores
Bonomo, F.; Marenco, J.; Saban, D.; Stier-Moses, N.E.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work. © 2011 Elsevier B.V. All rights reserved.
Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Marenco, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Saban, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Stier-Moses, N.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fuente
Discrete Appl Math 2012;160(18):2573-2590
Materia
Maximum edge subgraph problem
Polyhedral combinatorics
Quasi-cliques
Branch-and-cut algorithms
Computational studies
Integer programming formulations
Polyhedral approach
Polyhedral combinatorics
Polyhedral studies
Polytopes
Quasi-cliques
Separation problems
Social Network Analysis
Subgraph problems
Valid inequality
Integer programming
Linear programming
Social networking (online)
Computational complexity
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0166218X_v160_n18_p2573_Bonomo
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oai_identifier_str paperaa:paper_0166218X_v160_n18_p2573_Bonomo
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling A polyhedral study of the maximum edge subgraph problemBonomo, F.Marenco, J.Saban, D.Stier-Moses, N.E.Maximum edge subgraph problemPolyhedral combinatoricsQuasi-cliquesBranch-and-cut algorithmsComputational studiesInteger programming formulationsPolyhedral approachPolyhedral combinatoricsPolyhedral studiesPolytopesQuasi-cliquesSeparation problemsSocial Network AnalysisSubgraph problemsValid inequalityInteger programmingLinear programmingSocial networking (online)Computational complexityThe study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work. © 2011 Elsevier B.V. All rights reserved.Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Marenco, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Saban, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Stier-Moses, N.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2573_BonomoDiscrete Appl Math 2012;160(18):2573-2590reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2026-03-26T11:19:41Zpaperaa:paper_0166218X_v160_n18_p2573_BonomoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962026-03-26 11:19:42.698Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv A polyhedral study of the maximum edge subgraph problem
title A polyhedral study of the maximum edge subgraph problem
spellingShingle A polyhedral study of the maximum edge subgraph problem
Bonomo, F.
Maximum edge subgraph problem
Polyhedral combinatorics
Quasi-cliques
Branch-and-cut algorithms
Computational studies
Integer programming formulations
Polyhedral approach
Polyhedral combinatorics
Polyhedral studies
Polytopes
Quasi-cliques
Separation problems
Social Network Analysis
Subgraph problems
Valid inequality
Integer programming
Linear programming
Social networking (online)
Computational complexity
title_short A polyhedral study of the maximum edge subgraph problem
title_full A polyhedral study of the maximum edge subgraph problem
title_fullStr A polyhedral study of the maximum edge subgraph problem
title_full_unstemmed A polyhedral study of the maximum edge subgraph problem
title_sort A polyhedral study of the maximum edge subgraph problem
dc.creator.none.fl_str_mv Bonomo, F.
Marenco, J.
Saban, D.
Stier-Moses, N.E.
author Bonomo, F.
author_facet Bonomo, F.
Marenco, J.
Saban, D.
Stier-Moses, N.E.
author_role author
author2 Marenco, J.
Saban, D.
Stier-Moses, N.E.
author2_role author
author
author
dc.subject.none.fl_str_mv Maximum edge subgraph problem
Polyhedral combinatorics
Quasi-cliques
Branch-and-cut algorithms
Computational studies
Integer programming formulations
Polyhedral approach
Polyhedral combinatorics
Polyhedral studies
Polytopes
Quasi-cliques
Separation problems
Social Network Analysis
Subgraph problems
Valid inequality
Integer programming
Linear programming
Social networking (online)
Computational complexity
topic Maximum edge subgraph problem
Polyhedral combinatorics
Quasi-cliques
Branch-and-cut algorithms
Computational studies
Integer programming formulations
Polyhedral approach
Polyhedral combinatorics
Polyhedral studies
Polytopes
Quasi-cliques
Separation problems
Social Network Analysis
Subgraph problems
Valid inequality
Integer programming
Linear programming
Social networking (online)
Computational complexity
dc.description.none.fl_txt_mv The study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work. © 2011 Elsevier B.V. All rights reserved.
Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Marenco, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Saban, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Stier-Moses, N.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
description The study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work. © 2011 Elsevier B.V. All rights reserved.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2573_Bonomo
url http://hdl.handle.net/20.500.12110/paper_0166218X_v160_n18_p2573_Bonomo
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Discrete Appl Math 2012;160(18):2573-2590
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 13.332987

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