Improved algorithms for k-domination and total k-domination in proper interval graphs

Autores
Chiarelli, Nina; Hartinger, Tatiana Romina; Leoni, Valeria Alejandra; Lopez Pujato, María Inés; Milanič, Martin
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-dominating set, in a given graph, are referred to as k-domination, resp. total k-domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total k-domination). On the other hand, it follows from recent work by Kang et al. (2017) that these two families of problems are solvable in time O(|V(G)|6k+4) in the class of interval graphs. In this work, we develop faster algorithms for k-domination and total k-domination in the class of proper interval graphs. The algorithms run in time O(|V(G)|3k) for each fixed k≥1 and are also applicable to the weighted case.
Fil: Chiarelli, Nina. University of Primorska; Eslovenia
Fil: Hartinger, Tatiana Romina. University of Primorska; Eslovenia
Fil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Lopez Pujato, María Inés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina. Ministerio de Ciencia. Tecnología e Innovación Productiva. Agencia Nacional de Promoción Científica y Tecnológica; Argentina
Fil: Milanič, Martin. University of Primorska; Eslovenia
Materia
K-DOMINATION
TOTAL K-DOMINATION
PROPER INTERVAL GRAPH
POLYNOMIAL-TIME ALGORITHM
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:11336/99792
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Improved algorithms for k-domination and total k-domination in proper interval graphsChiarelli, NinaHartinger, Tatiana RominaLeoni, Valeria AlejandraLopez Pujato, María InésMilanič, MartinK-DOMINATIONTOTAL K-DOMINATIONPROPER INTERVAL GRAPHPOLYNOMIAL-TIME ALGORITHMhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-dominating set, in a given graph, are referred to as k-domination, resp. total k-domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total k-domination). On the other hand, it follows from recent work by Kang et al. (2017) that these two families of problems are solvable in time O(|V(G)|6k+4) in the class of interval graphs. In this work, we develop faster algorithms for k-domination and total k-domination in the class of proper interval graphs. The algorithms run in time O(|V(G)|3k) for each fixed k≥1 and are also applicable to the weighted case.Fil: Chiarelli, Nina. University of Primorska; EsloveniaFil: Hartinger, Tatiana Romina. University of Primorska; EsloveniaFil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Lopez Pujato, María Inés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina. Ministerio de Ciencia. Tecnología e Innovación Productiva. Agencia Nacional de Promoción Científica y Tecnológica; ArgentinaFil: Milanič, Martin. University of Primorska; EsloveniaSpringer2018-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/99792Chiarelli, Nina; Hartinger, Tatiana Romina; Leoni, Valeria Alejandra; Lopez Pujato, María Inés; Milanič, Martin; Improved algorithms for k-domination and total k-domination in proper interval graphs; Springer; Lecture Notes in Computer Science; 10856 LNCS; 7-2018; 290-3020302-9743CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/chapter/10.1007%2F978-3-319-96151-4_25info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-96151-4_25info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:00:54Zoai:ri.conicet.gov.ar:11336/99792instacron: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:34982025-09-10 13:00:54.839CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Improved algorithms for k-domination and total k-domination in proper interval graphs
title Improved algorithms for k-domination and total k-domination in proper interval graphs
spellingShingle Improved algorithms for k-domination and total k-domination in proper interval graphs
Chiarelli, Nina
K-DOMINATION
TOTAL K-DOMINATION
PROPER INTERVAL GRAPH
POLYNOMIAL-TIME ALGORITHM
title_short Improved algorithms for k-domination and total k-domination in proper interval graphs
title_full Improved algorithms for k-domination and total k-domination in proper interval graphs
title_fullStr Improved algorithms for k-domination and total k-domination in proper interval graphs
title_full_unstemmed Improved algorithms for k-domination and total k-domination in proper interval graphs
title_sort Improved algorithms for k-domination and total k-domination in proper interval graphs
dc.creator.none.fl_str_mv Chiarelli, Nina
Hartinger, Tatiana Romina
Leoni, Valeria Alejandra
Lopez Pujato, María Inés
Milanič, Martin
author Chiarelli, Nina
author_facet Chiarelli, Nina
Hartinger, Tatiana Romina
Leoni, Valeria Alejandra
Lopez Pujato, María Inés
Milanič, Martin
author_role author
author2 Hartinger, Tatiana Romina
Leoni, Valeria Alejandra
Lopez Pujato, María Inés
Milanič, Martin
author2_role author
author
author
author
dc.subject.none.fl_str_mv K-DOMINATION
TOTAL K-DOMINATION
PROPER INTERVAL GRAPH
POLYNOMIAL-TIME ALGORITHM
topic K-DOMINATION
TOTAL K-DOMINATION
PROPER INTERVAL GRAPH
POLYNOMIAL-TIME ALGORITHM
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-dominating set, in a given graph, are referred to as k-domination, resp. total k-domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total k-domination). On the other hand, it follows from recent work by Kang et al. (2017) that these two families of problems are solvable in time O(|V(G)|6k+4) in the class of interval graphs. In this work, we develop faster algorithms for k-domination and total k-domination in the class of proper interval graphs. The algorithms run in time O(|V(G)|3k) for each fixed k≥1 and are also applicable to the weighted case.
Fil: Chiarelli, Nina. University of Primorska; Eslovenia
Fil: Hartinger, Tatiana Romina. University of Primorska; Eslovenia
Fil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Lopez Pujato, María Inés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario; Argentina. Ministerio de Ciencia. Tecnología e Innovación Productiva. Agencia Nacional de Promoción Científica y Tecnológica; Argentina
Fil: Milanič, Martin. University of Primorska; Eslovenia
description Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating set, is a set of vertices such that every vertex of the graph has at least k neighbors in the set. The problems of finding the minimum size of a k-dominating, resp. total k-dominating set, in a given graph, are referred to as k-domination, resp. total k-domination. These generalizations of the classical domination and total domination problems are known to be NP-hard in the class of chordal graphs, and, more specifically, even in the classes of split graphs (both problems) and undirected path graphs (in the case of total k-domination). On the other hand, it follows from recent work by Kang et al. (2017) that these two families of problems are solvable in time O(|V(G)|6k+4) in the class of interval graphs. In this work, we develop faster algorithms for k-domination and total k-domination in the class of proper interval graphs. The algorithms run in time O(|V(G)|3k) for each fixed k≥1 and are also applicable to the weighted case.
publishDate 2018
dc.date.none.fl_str_mv 2018-07
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/11336/99792
Chiarelli, Nina; Hartinger, Tatiana Romina; Leoni, Valeria Alejandra; Lopez Pujato, María Inés; Milanič, Martin; Improved algorithms for k-domination and total k-domination in proper interval graphs; Springer; Lecture Notes in Computer Science; 10856 LNCS; 7-2018; 290-302
0302-9743
CONICET Digital
CONICET
url http://hdl.handle.net/11336/99792
identifier_str_mv Chiarelli, Nina; Hartinger, Tatiana Romina; Leoni, Valeria Alejandra; Lopez Pujato, María Inés; Milanič, Martin; Improved algorithms for k-domination and total k-domination in proper interval graphs; Springer; Lecture Notes in Computer Science; 10856 LNCS; 7-2018; 290-302
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%2F978-3-319-96151-4_25
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-96151-4_25
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 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 12.48226

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