Polyhedral study of the maximum common induced subgraph problem
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
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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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 |
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eng |
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eng |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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