The minimum stabbing triangulation problem: IP models and computational evaluation
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/1708 |
Resumo: | The minimum stabbing triangulation of a set of points in the plane (mstr) was previously investigated in the literature. The complexity of the mstr remains open and, to our knowledge, no exact algorithm was proposed and no computational results were reported earlier in the literature of the problem. This paper presents integer programming (ip) formulations for the mstr, that allow us to solve it exactly through ip branch-and-bound (b&b) algorithms. Moreover, one of these models is the basis for the development of a sophisticated Lagrangian heuristic for the problem. Computational tests were conducted with two instance classes comparing the performance of the latter algorithm against that of a standard (exact) b&b. The results reveal that the Lagrangian algorithm yielded solutions with minute, and often null, duality gaps for instances with several hundreds of points in small computation times. |
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Piva, BrenoSouza, Cid Carvalho de2016-03-16T21:41:28Z2016-03-16T21:41:28Z2012PIVA, B.; SOUZA, C. C. The minimum stabbing triangulation problem: IP models and computational evaluation. Lecture Notes in Computer Science, v. 7422, 2012. Disponível em: <http://dx.doi.org/10.1007/978-3-642-32147-4_5>. Acesso em: 16 mar. 2016.0302-9743https://ri.ufs.br/handle/riufs/1708© Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/978-3-642-32147-4_5The minimum stabbing triangulation of a set of points in the plane (mstr) was previously investigated in the literature. The complexity of the mstr remains open and, to our knowledge, no exact algorithm was proposed and no computational results were reported earlier in the literature of the problem. This paper presents integer programming (ip) formulations for the mstr, that allow us to solve it exactly through ip branch-and-bound (b&b) algorithms. Moreover, one of these models is the basis for the development of a sophisticated Lagrangian heuristic for the problem. Computational tests were conducted with two instance classes comparing the performance of the latter algorithm against that of a standard (exact) b&b. The results reveal that the Lagrangian algorithm yielded solutions with minute, and often null, duality gaps for instances with several hundreds of points in small computation times.Springer Berlin HeidelbergMinimum stabbing triangulationAlgoritmosInteger programmingProgramação linear inteiraThe minimum stabbing triangulation problem: IP models and computational evaluationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleengreponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessTHUMBNAILMinimumStabbingTriangulation.pdf.jpgMinimumStabbingTriangulation.pdf.jpgGenerated Thumbnailimage/jpeg1367https://ri.ufs.br/jspui/bitstream/riufs/1708/4/MinimumStabbingTriangulation.pdf.jpg54dc3e44de8455254642aaad610c585fMD54ORIGINALMinimumStabbingTriangulation.pdfMinimumStabbingTriangulation.pdfapplication/pdf162307https://ri.ufs.br/jspui/bitstream/riufs/1708/1/MinimumStabbingTriangulation.pdf5f6a01d3632593ca571c6185a66b7bb9MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://ri.ufs.br/jspui/bitstream/riufs/1708/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52TEXTMinimumStabbingTriangulation.pdf.txtMinimumStabbingTriangulation.pdf.txtExtracted texttext/plain32851https://ri.ufs.br/jspui/bitstream/riufs/1708/3/MinimumStabbingTriangulation.pdf.txte4d4ae80234c39f8285fa047d6aaf18eMD53riufs/17082016-03-17 02:00:18.3oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2016-03-17T05:00:18Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false |
dc.title.pt_BR.fl_str_mv |
The minimum stabbing triangulation problem: IP models and computational evaluation |
title |
The minimum stabbing triangulation problem: IP models and computational evaluation |
spellingShingle |
The minimum stabbing triangulation problem: IP models and computational evaluation Piva, Breno Minimum stabbing triangulation Algoritmos Integer programming Programação linear inteira |
title_short |
The minimum stabbing triangulation problem: IP models and computational evaluation |
title_full |
The minimum stabbing triangulation problem: IP models and computational evaluation |
title_fullStr |
The minimum stabbing triangulation problem: IP models and computational evaluation |
title_full_unstemmed |
The minimum stabbing triangulation problem: IP models and computational evaluation |
title_sort |
The minimum stabbing triangulation problem: IP models and computational evaluation |
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 |
Minimum stabbing triangulation Algoritmos Integer programming Programação linear inteira |
topic |
Minimum stabbing triangulation Algoritmos Integer programming Programação linear inteira |
description |
The minimum stabbing triangulation of a set of points in the plane (mstr) was previously investigated in the literature. The complexity of the mstr remains open and, to our knowledge, no exact algorithm was proposed and no computational results were reported earlier in the literature of the problem. This paper presents integer programming (ip) formulations for the mstr, that allow us to solve it exactly through ip branch-and-bound (b&b) algorithms. Moreover, one of these models is the basis for the development of a sophisticated Lagrangian heuristic for the problem. Computational tests were conducted with two instance classes comparing the performance of the latter algorithm against that of a standard (exact) b&b. The results reveal that the Lagrangian algorithm yielded solutions with minute, and often null, duality gaps for instances with several hundreds of points in small computation times. |
publishDate |
2012 |
dc.date.issued.fl_str_mv |
2012 |
dc.date.accessioned.fl_str_mv |
2016-03-16T21:41:28Z |
dc.date.available.fl_str_mv |
2016-03-16T21:41:28Z |
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. C. The minimum stabbing triangulation problem: IP models and computational evaluation. Lecture Notes in Computer Science, v. 7422, 2012. Disponível em: <http://dx.doi.org/10.1007/978-3-642-32147-4_5>. Acesso em: 16 mar. 2016. |
dc.identifier.uri.fl_str_mv |
https://ri.ufs.br/handle/riufs/1708 |
dc.identifier.issn.none.fl_str_mv |
0302-9743 |
dc.identifier.license.pt_BR.fl_str_mv |
© Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/978-3-642-32147-4_5 |
identifier_str_mv |
PIVA, B.; SOUZA, C. C. The minimum stabbing triangulation problem: IP models and computational evaluation. Lecture Notes in Computer Science, v. 7422, 2012. Disponível em: <http://dx.doi.org/10.1007/978-3-642-32147-4_5>. Acesso em: 16 mar. 2016. 0302-9743 © Springer International Publishing AG - Artigo publicado originalmente em: http://dx.doi.org/10.1007/978-3-642-32147-4_5 |
url |
https://ri.ufs.br/handle/riufs/1708 |
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eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Springer Berlin Heidelberg |
publisher.none.fl_str_mv |
Springer Berlin Heidelberg |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFS instname:Universidade Federal de Sergipe (UFS) instacron:UFS |
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UFS |
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