Exact Algorithms for Minimum Weighted Dominating Induced Matching

Autores
Lin, Min Chih; Mizrahi, Michel Jonathan; Szwarcfiter, Jayme L.
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G= (V, E) is a subset of edges E′⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of counting the number of dominating induced matchings and finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe three exact algorithms for general graphs. The first runs in linear time for a given vertex dominating set of fixed size of the graph. The second runs in polynomial time if the graph admits a polynomial number of maximal independent sets. The third one is an O∗(1. 1939 n) time and polynomial (linear) space, which improves over the existing algorithms for exactly solving this problem in general graphs.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
Materia
Dominating Induced Matchings
Exact Algorithms
Graph Theory
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:11336/60000
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/60000
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Exact Algorithms for Minimum Weighted Dominating Induced MatchingLin, Min ChihMizrahi, Michel JonathanSzwarcfiter, Jayme L.Dominating Induced MatchingsExact AlgorithmsGraph Theoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G= (V, E) is a subset of edges E′⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of counting the number of dominating induced matchings and finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe three exact algorithms for general graphs. The first runs in linear time for a given vertex dominating set of fixed size of the graph. The second runs in polynomial time if the graph admits a polynomial number of maximal independent sets. The third one is an O∗(1. 1939 n) time and polynomial (linear) space, which improves over the existing algorithms for exactly solving this problem in general graphs.Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; BrasilSpringer2017-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60000Lin, Min Chih; Mizrahi, Michel Jonathan; Szwarcfiter, Jayme L.; Exact Algorithms for Minimum Weighted Dominating Induced Matching; Springer; Algorithmica; 77; 3; 3-2017; 642-6600178-46171432-0541CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00453-015-0095-6info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00453-015-0095-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:38:05Zoai:ri.conicet.gov.ar:11336/60000instacron: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:34982025-09-29 09:38:05.654CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Exact Algorithms for Minimum Weighted Dominating Induced Matching
title Exact Algorithms for Minimum Weighted Dominating Induced Matching
spellingShingle Exact Algorithms for Minimum Weighted Dominating Induced Matching
Lin, Min Chih
Dominating Induced Matchings
Exact Algorithms
Graph Theory
title_short Exact Algorithms for Minimum Weighted Dominating Induced Matching
title_full Exact Algorithms for Minimum Weighted Dominating Induced Matching
title_fullStr Exact Algorithms for Minimum Weighted Dominating Induced Matching
title_full_unstemmed Exact Algorithms for Minimum Weighted Dominating Induced Matching
title_sort Exact Algorithms for Minimum Weighted Dominating Induced Matching
dc.creator.none.fl_str_mv Lin, Min Chih
Mizrahi, Michel Jonathan
Szwarcfiter, Jayme L.
author Lin, Min Chih
author_facet Lin, Min Chih
Mizrahi, Michel Jonathan
Szwarcfiter, Jayme L.
author_role author
author2 Mizrahi, Michel Jonathan
Szwarcfiter, Jayme L.
author2_role author
author
dc.subject.none.fl_str_mv Dominating Induced Matchings
Exact Algorithms
Graph Theory
topic Dominating Induced Matchings
Exact Algorithms
Graph Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G= (V, E) is a subset of edges E′⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of counting the number of dominating induced matchings and finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe three exact algorithms for general graphs. The first runs in linear time for a given vertex dominating set of fixed size of the graph. The second runs in polynomial time if the graph admits a polynomial number of maximal independent sets. The third one is an O∗(1. 1939 n) time and polynomial (linear) space, which improves over the existing algorithms for exactly solving this problem in general graphs.
Fil: Lin, Min Chih. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Mizrahi, Michel Jonathan. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Szwarcfiter, Jayme L.. Universidade Federal do Rio de Janeiro; Brasil
description Say that an edge of a graph G dominates itself and every other edge sharing a vertex of it. An edge dominating set of a graph G= (V, E) is a subset of edges E′⊆ E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E′ then E′ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of counting the number of dominating induced matchings and finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe three exact algorithms for general graphs. The first runs in linear time for a given vertex dominating set of fixed size of the graph. The second runs in polynomial time if the graph admits a polynomial number of maximal independent sets. The third one is an O∗(1. 1939 n) time and polynomial (linear) space, which improves over the existing algorithms for exactly solving this problem in general graphs.
publishDate 2017
dc.date.none.fl_str_mv 2017-03
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/11336/60000
Lin, Min Chih; Mizrahi, Michel Jonathan; Szwarcfiter, Jayme L.; Exact Algorithms for Minimum Weighted Dominating Induced Matching; Springer; Algorithmica; 77; 3; 3-2017; 642-660
0178-4617
1432-0541
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60000
identifier_str_mv Lin, Min Chih; Mizrahi, Michel Jonathan; Szwarcfiter, Jayme L.; Exact Algorithms for Minimum Weighted Dominating Induced Matching; Springer; Algorithmica; 77; 3; 3-2017; 642-660
0178-4617
1432-0541
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00453-015-0095-6
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00453-015-0095-6
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 13.070432

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