Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs

Autores
Leoni, Valeria Alejandra; Dobson, Maria Patricia
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a positive integer k, the {k}-packing function problem ({k}PF) is to find in a given graph G, a function f of maximum weight that assigns a non-negative integer to the vertices of G in such a way that the sum of f(v) over each closed neighborhood is at most k. This notion was recently introduced as a variation of the k-limited packing problem (kLP) introduced in 2010, where the function was supposed to assign a value in {0, 1}. For all the graph classes explored up to now, {k}PF and kLP have the same computational complexity. It is an open problem to determine a graph class where one of them is NP-complete and the other, polynomially solvable. In this work, we first prove that {k}PF is NP-complete for bipartite graphs, as kLP is known to be. We also obtain new graph classes where the complexity of these problems would coincide.
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
Bipartite Graph
Computational Complexity
F-Free Graph
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:11336/52744
Acceder
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spelling Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphsLeoni, Valeria AlejandraDobson, Maria PatriciaBipartite GraphComputational ComplexityF-Free Graphhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1Given a positive integer k, the {k}-packing function problem ({k}PF) is to find in a given graph G, a function f of maximum weight that assigns a non-negative integer to the vertices of G in such a way that the sum of f(v) over each closed neighborhood is at most k. This notion was recently introduced as a variation of the k-limited packing problem (kLP) introduced in 2010, where the function was supposed to assign a value in {0, 1}. For all the graph classes explored up to now, {k}PF and kLP have the same computational complexity. It is an open problem to determine a graph class where one of them is NP-complete and the other, polynomially solvable. In this work, we first prove that {k}PF is NP-complete for bipartite graphs, as kLP is known to be. We also obtain new graph classes where the complexity of these problems would coincide.Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaSpringer2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/52744Leoni, Valeria Alejandra; Dobson, Maria Patricia; Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs; Springer; Lecture Notes in Computer Science; 9849; 5-2016; 160-1650302-9743CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/chapter/10.1007%2F978-3-319-45587-7_14info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-45587-7_14info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T11:11:39Zoai:ri.conicet.gov.ar:11336/52744instacron: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:34982025-10-29 11:11:39.422CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
title Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
spellingShingle Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
Leoni, Valeria Alejandra
Bipartite Graph
Computational Complexity
F-Free Graph
title_short Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
title_full Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
title_fullStr Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
title_full_unstemmed Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
title_sort Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs
dc.creator.none.fl_str_mv Leoni, Valeria Alejandra
Dobson, Maria Patricia
author Leoni, Valeria Alejandra
author_facet Leoni, Valeria Alejandra
Dobson, Maria Patricia
author_role author
author2 Dobson, Maria Patricia
author2_role author
dc.subject.none.fl_str_mv Bipartite Graph
Computational Complexity
F-Free Graph
topic Bipartite Graph
Computational Complexity
F-Free Graph
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a positive integer k, the {k}-packing function problem ({k}PF) is to find in a given graph G, a function f of maximum weight that assigns a non-negative integer to the vertices of G in such a way that the sum of f(v) over each closed neighborhood is at most k. This notion was recently introduced as a variation of the k-limited packing problem (kLP) introduced in 2010, where the function was supposed to assign a value in {0, 1}. For all the graph classes explored up to now, {k}PF and kLP have the same computational complexity. It is an open problem to determine a graph class where one of them is NP-complete and the other, polynomially solvable. In this work, we first prove that {k}PF is NP-complete for bipartite graphs, as kLP is known to be. We also obtain new graph classes where the complexity of these problems would coincide.
Fil: Leoni, Valeria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Dobson, Maria Patricia. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description Given a positive integer k, the {k}-packing function problem ({k}PF) is to find in a given graph G, a function f of maximum weight that assigns a non-negative integer to the vertices of G in such a way that the sum of f(v) over each closed neighborhood is at most k. This notion was recently introduced as a variation of the k-limited packing problem (kLP) introduced in 2010, where the function was supposed to assign a value in {0, 1}. For all the graph classes explored up to now, {k}PF and kLP have the same computational complexity. It is an open problem to determine a graph class where one of them is NP-complete and the other, polynomially solvable. In this work, we first prove that {k}PF is NP-complete for bipartite graphs, as kLP is known to be. We also obtain new graph classes where the complexity of these problems would coincide.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
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/11336/52744
Leoni, Valeria Alejandra; Dobson, Maria Patricia; Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs; Springer; Lecture Notes in Computer Science; 9849; 5-2016; 160-165
0302-9743
CONICET Digital
CONICET
url http://hdl.handle.net/11336/52744
identifier_str_mv Leoni, Valeria Alejandra; Dobson, Maria Patricia; Towards a polynomial equivalence between {k}-packing functions and k-limited packings in graphs; Springer; Lecture Notes in Computer Science; 9849; 5-2016; 160-165
0302-9743
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/chapter/10.1007%2F978-3-319-45587-7_14
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-45587-7_14
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 13.10058

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