Polyhedral study of the maximum common induced subgraph problem

Detalhes bibliográficos
Autor(a) principal: Piva, Breno
Data de Publicação: 2012
Outros Autores: Souza, Cid Carvalho de
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFS
Texto Completo: https://ri.ufs.br/handle/riufs/1705
Resumo: In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Maximum Clique problem. We report on computational results of branch-and-bound (B&B) and branch-and-cut (B&C) algorithms we implemented and compare them to those yielded by an existing combinatorial algorithm.
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spelling Piva, BrenoSouza, Cid Carvalho de2016-03-16T20:56:51Z2016-03-16T20:56:51Z2012-10PIVA, B; SOUZA, C. Polyhedral study of the maximum common induced subgraph problem. Annals of Operations Research, v. 199, n. 1, p. 77-102, out. 2012. Disponível em: <http://dx.doi.org/10.1007/s10479-011-1019-8>. Acesso em: 16 mar. 2016.1572-9338https://ri.ufs.br/handle/riufs/1705© Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/s10479-011-1019-8In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Maximum Clique problem. We report on computational results of branch-and-bound (B&B) and branch-and-cut (B&C) algorithms we implemented and compare them to those yielded by an existing combinatorial algorithm.Financial support by Fapesp, grant number 2007/53617-4 (10/2007 - 02/2009) and CNPq, grants number 132034/2007-7 (03/2007 - 09/2007), 301732/2007-8 and 472504/2007-0.SpringerMaximum common induced subgraphPolyhedral combinatoricsInteger programmingBranch and Bound algorithmBranch and Cut algorithmMaximum cliqueCombinatória poliédricaMáximo subgrafo comumProgramação linear inteiraAlgoritmo Branch and BoundAlgoritmo Branch and CutPolyhedral study of the maximum common induced subgraph probleminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleengreponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessTHUMBNAILPolyhedralStudyProblem.pdf.jpgPolyhedralStudyProblem.pdf.jpgGenerated Thumbnailimage/jpeg1278https://ri.ufs.br/jspui/bitstream/riufs/1705/4/PolyhedralStudyProblem.pdf.jpgf5d803108e063a85fd35f80cf0646df7MD54ORIGINALPolyhedralStudyProblem.pdfPolyhedralStudyProblem.pdfapplication/pdf284850https://ri.ufs.br/jspui/bitstream/riufs/1705/1/PolyhedralStudyProblem.pdfe403a32c40338e9a709945b068cea7edMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://ri.ufs.br/jspui/bitstream/riufs/1705/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52TEXTPolyhedralStudyProblem.pdf.txtPolyhedralStudyProblem.pdf.txtExtracted texttext/plain80345https://ri.ufs.br/jspui/bitstream/riufs/1705/3/PolyhedralStudyProblem.pdf.txt0c7d71096c31fce6dc3707051e27e410MD53riufs/17052017-11-17 21:33:02.108oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2017-11-18T00:33:02Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Polyhedral study of the maximum common induced subgraph problem
title Polyhedral study of the maximum common induced subgraph problem
spellingShingle Polyhedral study of the maximum common induced subgraph problem
Piva, Breno
Maximum common induced subgraph
Polyhedral combinatorics
Integer programming
Branch and Bound algorithm
Branch and Cut algorithm
Maximum clique
Combinatória poliédrica
Máximo subgrafo comum
Programação linear inteira
Algoritmo Branch and Bound
Algoritmo Branch and Cut
title_short Polyhedral study of the maximum common induced subgraph problem
title_full Polyhedral study of the maximum common induced subgraph problem
title_fullStr Polyhedral study of the maximum common induced subgraph problem
title_full_unstemmed Polyhedral study of the maximum common induced subgraph problem
title_sort Polyhedral study of the maximum common induced subgraph problem
author Piva, Breno
author_facet Piva, Breno
Souza, Cid Carvalho de
author_role author
author2 Souza, Cid Carvalho de
author2_role author
dc.contributor.author.fl_str_mv Piva, Breno
Souza, Cid Carvalho de
dc.subject.por.fl_str_mv Maximum common induced subgraph
Polyhedral combinatorics
Integer programming
Branch and Bound algorithm
Branch and Cut algorithm
Maximum clique
Combinatória poliédrica
Máximo subgrafo comum
Programação linear inteira
Algoritmo Branch and Bound
Algoritmo Branch and Cut
topic Maximum common induced subgraph
Polyhedral combinatorics
Integer programming
Branch and Bound algorithm
Branch and Cut algorithm
Maximum clique
Combinatória poliédrica
Máximo subgrafo comum
Programação linear inteira
Algoritmo Branch and Bound
Algoritmo Branch and Cut
description In this paper we present an exact algorithm for the Maximum Common Induced Subgraph Problem (MCIS) by addressing it directly, using Integer Programming (IP) and polyhedral combinatorics. We study the MCIS polytope and introduce strong valid inequalities, some of which we prove to define facets. Besides, we show an equivalence between our IP model for MCIS and a well-known formulation for the Maximum Clique problem. We report on computational results of branch-and-bound (B&B) and branch-and-cut (B&C) algorithms we implemented and compare them to those yielded by an existing combinatorial algorithm.
publishDate 2012
dc.date.issued.fl_str_mv 2012-10
dc.date.accessioned.fl_str_mv 2016-03-16T20:56:51Z
dc.date.available.fl_str_mv 2016-03-16T20:56:51Z
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.citation.fl_str_mv PIVA, B; SOUZA, C. Polyhedral study of the maximum common induced subgraph problem. Annals of Operations Research, v. 199, n. 1, p. 77-102, out. 2012. Disponível em: <http://dx.doi.org/10.1007/s10479-011-1019-8>. Acesso em: 16 mar. 2016.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/handle/riufs/1705
dc.identifier.issn.none.fl_str_mv 1572-9338
dc.identifier.license.pt_BR.fl_str_mv © Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/s10479-011-1019-8
identifier_str_mv PIVA, B; SOUZA, C. Polyhedral study of the maximum common induced subgraph problem. Annals of Operations Research, v. 199, n. 1, p. 77-102, out. 2012. Disponível em: <http://dx.doi.org/10.1007/s10479-011-1019-8>. Acesso em: 16 mar. 2016.
1572-9338
© Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/s10479-011-1019-8
url https://ri.ufs.br/handle/riufs/1705
dc.language.iso.fl_str_mv eng
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
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institution UFS
reponame_str Repositório Institucional da UFS
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