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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/15019
Ver los metadatos del registro completo
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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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.22299 |