A Branch and Price Algorithm for List Coloring Problem

Autores
Lucci, Mauro; Nasini, Graciela Leonor; Severin, Daniel Esteban
Año de publicación
2019
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.
Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)
Belo Horizonte
Brasil
Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior
Conselho Nacional de Desenvolvimento Científico e Técnologico do Brasil
Universidade Federal de Minas Gerais
Materia
List Coloring
Branch and Price
Weighted Problem
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:11336/129574
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/129574
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Branch and Price Algorithm for List Coloring ProblemLucci, MauroNasini, Graciela LeonorSeverin, Daniel EstebanList ColoringBranch and PriceWeighted Problemhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)Belo HorizonteBrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorConselho Nacional de Desenvolvimento Científico e Técnologico do BrasilUniversidade Federal de Minas GeraisElsevier2019info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectSimposioJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/129574A Branch and Price Algorithm for List Coloring Problem; 10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 613-6241571-0661CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.entcs.2019.08.054info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1571066119301057Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:50:18Zoai:ri.conicet.gov.ar:11336/129574instacron: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 09:50:18.485CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Branch and Price Algorithm for List Coloring Problem
title A Branch and Price Algorithm for List Coloring Problem
spellingShingle A Branch and Price Algorithm for List Coloring Problem
Lucci, Mauro
List Coloring
Branch and Price
Weighted Problem
title_short A Branch and Price Algorithm for List Coloring Problem
title_full A Branch and Price Algorithm for List Coloring Problem
title_fullStr A Branch and Price Algorithm for List Coloring Problem
title_full_unstemmed A Branch and Price Algorithm for List Coloring Problem
title_sort A Branch and Price Algorithm for List Coloring Problem
dc.creator.none.fl_str_mv Lucci, Mauro
Nasini, Graciela Leonor
Severin, Daniel Esteban
author Lucci, Mauro
author_facet Lucci, Mauro
Nasini, Graciela Leonor
Severin, Daniel Esteban
author_role author
author2 Nasini, Graciela Leonor
Severin, Daniel Esteban
author2_role author
author
dc.subject.none.fl_str_mv List Coloring
Branch and Price
Weighted Problem
topic List Coloring
Branch and Price
Weighted Problem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.
Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)
Belo Horizonte
Brasil
Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior
Conselho Nacional de Desenvolvimento Científico e Técnologico do Brasil
Universidade Federal de Minas Gerais
description Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Simposio
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/129574
A Branch and Price Algorithm for List Coloring Problem; 10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 613-624
1571-0661
CONICET Digital
CONICET
url http://hdl.handle.net/11336/129574
identifier_str_mv A Branch and Price Algorithm for List Coloring Problem; 10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019); Belo Horizonte; Brasil; 2019; 613-624
1571-0661
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.entcs.2019.08.054
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S1571066119301057
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.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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