Approximated algorithms for the Minimum Dilation Triangulation Problem

Autores
Dorzán, Maria Gisela; Leguizamon, Mario Guillermo; Mezura Montes, Efrén; Hernández Peñalver, Gregorio
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The complexity status of the Minimum Dilation Triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the Sequential Parameter Optimization Toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.
Fil: Dorzán, Maria Gisela. Universidad Nacional de San Luis; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis; Argentina
Fil: Leguizamon, Mario Guillermo. Universidad Nacional de San Luis; Argentina
Fil: Mezura Montes, Efrén. Universidad Veracruzana; México
Fil: Hernández Peñalver, Gregorio. Universidad Politecnica de Madrid; España
Materia
Computational Geometry
Metaheuristics
Triangulation
Minimum Dilation
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:11336/7565
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/7565
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Approximated algorithms for the Minimum Dilation Triangulation ProblemDorzán, Maria GiselaLeguizamon, Mario GuillermoMezura Montes, EfrénHernández Peñalver, GregorioComputational GeometryMetaheuristicsTriangulationMinimum Dilationhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1The complexity status of the Minimum Dilation Triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the Sequential Parameter Optimization Toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.Fil: Dorzán, Maria Gisela. Universidad Nacional de San Luis; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis; ArgentinaFil: Leguizamon, Mario Guillermo. Universidad Nacional de San Luis; ArgentinaFil: Mezura Montes, Efrén. Universidad Veracruzana; MéxicoFil: Hernández Peñalver, Gregorio. Universidad Politecnica de Madrid; EspañaSpringer2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/7565Dorzán, Maria Gisela; Leguizamon, Mario Guillermo; Mezura Montes, Efrén; Hernández Peñalver, Gregorio; Approximated algorithms for the Minimum Dilation Triangulation Problem; Springer; Journal Of Heuristics; 20; 2; 1-2014; 189-2091381-1231enginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10732-014-9237-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s10732-014-9237-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:25Zoai:ri.conicet.gov.ar:11336/7565instacron: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:34982025-09-29 10:18:25.879CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximated algorithms for the Minimum Dilation Triangulation Problem
title Approximated algorithms for the Minimum Dilation Triangulation Problem
spellingShingle Approximated algorithms for the Minimum Dilation Triangulation Problem
Dorzán, Maria Gisela
Computational Geometry
Metaheuristics
Triangulation
Minimum Dilation
title_short Approximated algorithms for the Minimum Dilation Triangulation Problem
title_full Approximated algorithms for the Minimum Dilation Triangulation Problem
title_fullStr Approximated algorithms for the Minimum Dilation Triangulation Problem
title_full_unstemmed Approximated algorithms for the Minimum Dilation Triangulation Problem
title_sort Approximated algorithms for the Minimum Dilation Triangulation Problem
dc.creator.none.fl_str_mv Dorzán, Maria Gisela
Leguizamon, Mario Guillermo
Mezura Montes, Efrén
Hernández Peñalver, Gregorio
author Dorzán, Maria Gisela
author_facet Dorzán, Maria Gisela
Leguizamon, Mario Guillermo
Mezura Montes, Efrén
Hernández Peñalver, Gregorio
author_role author
author2 Leguizamon, Mario Guillermo
Mezura Montes, Efrén
Hernández Peñalver, Gregorio
author2_role author
author
author
dc.subject.none.fl_str_mv Computational Geometry
Metaheuristics
Triangulation
Minimum Dilation
topic Computational Geometry
Metaheuristics
Triangulation
Minimum Dilation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The complexity status of the Minimum Dilation Triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the Sequential Parameter Optimization Toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.
Fil: Dorzán, Maria Gisela. Universidad Nacional de San Luis; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis; Argentina
Fil: Leguizamon, Mario Guillermo. Universidad Nacional de San Luis; Argentina
Fil: Mezura Montes, Efrén. Universidad Veracruzana; México
Fil: Hernández Peñalver, Gregorio. Universidad Politecnica de Madrid; España
description The complexity status of the Minimum Dilation Triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial approach, we design a greedy strategy able to obtain approximate solutions to the optimal ones in a simple way. We also propose an operator to generate the neighborhood which is used in different algorithms: Local Search, Iterated Local Search, and Simulated Annealing. Besides, we present an algorithm called Random Local Search where good and bad solutions are accepted using the previous mentioned operator. For the experimental study we have created a set of problem instances since no reference to benchmarks for these problems were found in the literature. We use the Sequential Parameter Optimization Toolbox for tuning the parameters of the SA algorithm. We compare our results with those obtained by the OV-MDT algorithm that uses the obstacle value to sort the edges in the constructive process. This is the only available algorithm found in the literature. Through the experimental evaluation and statistical analysis, we assess the performance of the proposed algorithms using this operator.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/7565
Dorzán, Maria Gisela; Leguizamon, Mario Guillermo; Mezura Montes, Efrén; Hernández Peñalver, Gregorio; Approximated algorithms for the Minimum Dilation Triangulation Problem; Springer; Journal Of Heuristics; 20; 2; 1-2014; 189-209
1381-1231
url http://hdl.handle.net/11336/7565
identifier_str_mv Dorzán, Maria Gisela; Leguizamon, Mario Guillermo; Mezura Montes, Efrén; Hernández Peñalver, Gregorio; Approximated algorithms for the Minimum Dilation Triangulation Problem; Springer; Journal Of Heuristics; 20; 2; 1-2014; 189-209
1381-1231
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s10732-014-9237-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10732-014-9237-2
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 Springer
publisher.none.fl_str_mv Springer
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 13.069144

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