An O*(1.1939n) time algorithm for minimum weighted dominating induced matching

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...

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Autores principales: Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L.
Formato: SER
Materias:
branch & reduce
dominating induced matchings
exact algorithms
Edge dominating set
Edge sharing
Exact algorithms
General graph
Graph G
Induced matchings
NP Complete
Time algorithms
Algorithms
Graph theory
Problem solving
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03029743_v8283LNCS_n_p558_Lin
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_03029743_v8283LNCS_n_p558_Lin
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spelling todo:paper_03029743_v8283LNCS_n_p558_Lin2023-10-03T15:19:35Z An O*(1.1939n) time algorithm for minimum weighted dominating induced matching Lin, M.C. Mizrahi, M.J. Szwarcfiter, J.L. branch & reduce dominating induced matchings exact algorithms Edge dominating set Edge sharing Exact algorithms General graph Graph G Induced matchings NP Complete Time algorithms Algorithms Graph theory Problem solving 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 finding a minimum weighted dominating induced matching, if any, and counting the number of dominating induced matchings of a graph with weighted edges. We describe an exact algorithm for general graphs that runs in O*(1.1939 n) time and polynomial (linear) space, for solving these problems. This improves over the existing exact algorithms for the problems in consideration. © 2013 Springer-Verlag. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03029743_v8283LNCS_n_p558_Lin
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic branch & reduce
dominating induced matchings
exact algorithms
Edge dominating set
Edge sharing
Exact algorithms
General graph
Graph G
Induced matchings
NP Complete
Time algorithms
Algorithms
Graph theory
Problem solving
spellingShingle branch & reduce
dominating induced matchings
exact algorithms
Edge dominating set
Edge sharing
Exact algorithms
General graph
Graph G
Induced matchings
NP Complete
Time algorithms
Algorithms
Graph theory
Problem solving
Lin, M.C.
Mizrahi, M.J.
Szwarcfiter, J.L.
An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
topic_facet branch & reduce
dominating induced matchings
exact algorithms
Edge dominating set
Edge sharing
Exact algorithms
General graph
Graph G
Induced matchings
NP Complete
Time algorithms
Algorithms
Graph theory
Problem solving
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 finding a minimum weighted dominating induced matching, if any, and counting the number of dominating induced matchings of a graph with weighted edges. We describe an exact algorithm for general graphs that runs in O*(1.1939 n) time and polynomial (linear) space, for solving these problems. This improves over the existing exact algorithms for the problems in consideration. © 2013 Springer-Verlag.
format SER
author Lin, M.C.
Mizrahi, M.J.
Szwarcfiter, J.L.
author_facet Lin, M.C.
Mizrahi, M.J.
Szwarcfiter, J.L.
author_sort Lin, M.C.
title An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
title_short An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
title_full An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
title_fullStr An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
title_full_unstemmed An O*(1.1939n) time algorithm for minimum weighted dominating induced matching
title_sort o*(1.1939n) time algorithm for minimum weighted dominating induced matching
url http://hdl.handle.net/20.500.12110/paper_03029743_v8283LNCS_n_p558_Lin
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