Minimum sum set coloring of trees and line graphs of trees

Autores
Bonomo, Flavia; Duran, Guillermo Alfredo; Marenco, Javier; Valencia Pabon, Mario
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Marenco, Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-nord; Francia
Materia
Graph Coloring
Minimum Sum Coloring
Set-Coloring
Trees
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15019

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network_name_str CONICET Digital (CONICET)
spelling Minimum sum set coloring of trees and line graphs of treesBonomo, FlaviaDuran, Guillermo AlfredoMarenco, JavierValencia Pabon, MarioGraph ColoringMinimum Sum ColoringSet-ColoringTreeshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1https://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Marenco, Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Valencia Pabon, Mario. Universite de Paris 13-nord; FranciaElsevier2011-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15019Bonomo, Flavia; Duran, Guillermo Alfredo; Marenco, Javier; Valencia Pabon, Mario; Minimum sum set coloring of trees and line graphs of trees; Elsevier; Discrete Applied Mathematics; 159; 5; 1-2011; 288-2940166-218Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2010.11.018info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X10004014info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:15:49Zoai:ri.conicet.gov.ar:11336/15019instacron: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:34982025-10-15 15:15:49.76CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Minimum sum set coloring of trees and line graphs of trees
title Minimum sum set coloring of trees and line graphs of trees
spellingShingle Minimum sum set coloring of trees and line graphs of trees
Bonomo, Flavia
Graph Coloring
Minimum Sum Coloring
Set-Coloring
Trees
title_short Minimum sum set coloring of trees and line graphs of trees
title_full Minimum sum set coloring of trees and line graphs of trees
title_fullStr Minimum sum set coloring of trees and line graphs of trees
title_full_unstemmed Minimum sum set coloring of trees and line graphs of trees
title_sort Minimum sum set coloring of trees and line graphs of trees
dc.creator.none.fl_str_mv Bonomo, Flavia
Duran, Guillermo Alfredo
Marenco, Javier
Valencia Pabon, Mario
author Bonomo, Flavia
author_facet Bonomo, Flavia
Duran, Guillermo Alfredo
Marenco, Javier
Valencia Pabon, Mario
author_role author
author2 Duran, Guillermo Alfredo
Marenco, Javier
Valencia Pabon, Mario
author2_role author
author
author
dc.subject.none.fl_str_mv Graph Coloring
Minimum Sum Coloring
Set-Coloring
Trees
topic Graph Coloring
Minimum Sum Coloring
Set-Coloring
Trees
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Duran, Guillermo Alfredo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Marenco, Javier. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Valencia Pabon, Mario. Universite de Paris 13-nord; Francia
description In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
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/11336/15019
Bonomo, Flavia; Duran, Guillermo Alfredo; Marenco, Javier; Valencia Pabon, Mario; Minimum sum set coloring of trees and line graphs of trees; Elsevier; Discrete Applied Mathematics; 159; 5; 1-2011; 288-294
0166-218X
url http://hdl.handle.net/11336/15019
identifier_str_mv Bonomo, Flavia; Duran, Guillermo Alfredo; Marenco, Javier; Valencia Pabon, Mario; Minimum sum set coloring of trees and line graphs of trees; Elsevier; Discrete Applied Mathematics; 159; 5; 1-2011; 288-294
0166-218X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.dam.2010.11.018
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0166218X10004014
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
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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