Complexity of the cluster deletion problem on subclasses of chordal graphs

Autores
Bonomo, Flavia; Duran, Guillermo Alfredo; Valencia Pabon, Mario
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to minimize the total weight of edges outside the clusters. The decision version of this optimization problem is known to be NP-complete even for unweighted graphs and has been studied extensively. We investigate the complexity of the decision CD problem for the family of chordal graphs, showing that it is NP-complete for weighted split graphs, weighted interval graphs and unweighted chordal graphs. We also prove that the problem is NP-complete for weighted cographs. Some polynomial-time solvable cases of the optimization problem are also identified, in particular CD for unweighted split graphs, unweighted proper interval graphs and weighted block graphs.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-Nord; Francia
Materia
Block Graphs
Cliques
Edge-Deletion
Cluster Deletion
Interval Graphs
Split Graphs
Submodular Functions
Chordal Graphs
Cographs
Np-Completeness
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18896
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18896
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Complexity of the cluster deletion problem on subclasses of chordal graphsBonomo, FlaviaDuran, Guillermo AlfredoValencia Pabon, MarioBlock GraphsCliquesEdge-DeletionCluster DeletionInterval GraphsSplit GraphsSubmodular FunctionsChordal GraphsCographsNp-Completenesshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to minimize the total weight of edges outside the clusters. The decision version of this optimization problem is known to be NP-complete even for unweighted graphs and has been studied extensively. We investigate the complexity of the decision CD problem for the family of chordal graphs, showing that it is NP-complete for weighted split graphs, weighted interval graphs and unweighted chordal graphs. We also prove that the problem is NP-complete for weighted cographs. Some polynomial-time solvable cases of the optimization problem are also identified, in particular CD for unweighted split graphs, unweighted proper interval graphs and weighted block graphs.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Valencia Pabon, Mario. Universite de Paris 13-Nord; FranciaElsevier Science2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18896Bonomo, Flavia; Duran, Guillermo Alfredo; Valencia Pabon, Mario; Complexity of the cluster deletion problem on subclasses of chordal graphs; Elsevier Science; Theoretical Computer Science; 600; 10-2015; 59-690304-3975CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2015.07.001info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397515005800info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:09Zoai:ri.conicet.gov.ar:11336/18896instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:57:10.11CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Complexity of the cluster deletion problem on subclasses of chordal graphs
title Complexity of the cluster deletion problem on subclasses of chordal graphs
spellingShingle Complexity of the cluster deletion problem on subclasses of chordal graphs
Bonomo, Flavia
Block Graphs
Cliques
Edge-Deletion
Cluster Deletion
Interval Graphs
Split Graphs
Submodular Functions
Chordal Graphs
Cographs
Np-Completeness
title_short Complexity of the cluster deletion problem on subclasses of chordal graphs
title_full Complexity of the cluster deletion problem on subclasses of chordal graphs
title_fullStr Complexity of the cluster deletion problem on subclasses of chordal graphs
title_full_unstemmed Complexity of the cluster deletion problem on subclasses of chordal graphs
title_sort Complexity of the cluster deletion problem on subclasses of chordal graphs
dc.creator.none.fl_str_mv Bonomo, Flavia
Duran, Guillermo Alfredo
Valencia Pabon, Mario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Duran, Guillermo Alfredo
Valencia Pabon, Mario
author_role author
author2 Duran, Guillermo Alfredo
Valencia Pabon, Mario
author2_role author
author
dc.subject.none.fl_str_mv Block Graphs
Cliques
Edge-Deletion
Cluster Deletion
Interval Graphs
Split Graphs
Submodular Functions
Chordal Graphs
Cographs
Np-Completeness
topic Block Graphs
Cliques
Edge-Deletion
Cluster Deletion
Interval Graphs
Split Graphs
Submodular Functions
Chordal Graphs
Cographs
Np-Completeness
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to minimize the total weight of edges outside the clusters. The decision version of this optimization problem is known to be NP-complete even for unweighted graphs and has been studied extensively. We investigate the complexity of the decision CD problem for the family of chordal graphs, showing that it is NP-complete for weighted split graphs, weighted interval graphs and unweighted chordal graphs. We also prove that the problem is NP-complete for weighted cographs. Some polynomial-time solvable cases of the optimization problem are also identified, in particular CD for unweighted split graphs, unweighted proper interval graphs and weighted block graphs.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-Nord; Francia
description We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to minimize the total weight of edges outside the clusters. The decision version of this optimization problem is known to be NP-complete even for unweighted graphs and has been studied extensively. We investigate the complexity of the decision CD problem for the family of chordal graphs, showing that it is NP-complete for weighted split graphs, weighted interval graphs and unweighted chordal graphs. We also prove that the problem is NP-complete for weighted cographs. Some polynomial-time solvable cases of the optimization problem are also identified, in particular CD for unweighted split graphs, unweighted proper interval graphs and weighted block graphs.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/18896
Bonomo, Flavia; Duran, Guillermo Alfredo; Valencia Pabon, Mario; Complexity of the cluster deletion problem on subclasses of chordal graphs; Elsevier Science; Theoretical Computer Science; 600; 10-2015; 59-69
0304-3975
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18896
identifier_str_mv Bonomo, Flavia; Duran, Guillermo Alfredo; Valencia Pabon, Mario; Complexity of the cluster deletion problem on subclasses of chordal graphs; Elsevier Science; Theoretical Computer Science; 600; 10-2015; 59-69
0304-3975
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.tcs.2015.07.001
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0304397515005800
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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