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Abstract:

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. © 2015, Springer Science+Business Media New York.

Registro:

Documento: Artículo
Título:Exact Algorithms for Minimum Weighted Dominating Induced Matching
Autor:Lin, M.C.; Mizrahi, M.J.; Szwarcfiter, J.L.
Filiación:CONICET, Instituto de Cálculo, Buenos Aires, Argentina
Departamento de Computación, Universidad de Buenos Aires, Buenos Aires, Argentina
I. Mat., COPPE and NCE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
Instituto Nacional de Metrologia, Qualidade e Tecnologia, Rio de Janeiro, Brazil
Palabras clave:Dominating induced matchings; Exact algorithms; Graph theory; Algorithms; Polynomial approximation; Polynomials; Problem solving; Dominating sets; Edge dominating set; Exact algorithms; General graph; Induced matchings; Maximal independent set; Polynomial number; Polynomial-time; Graph theory
Año:2017
Volumen:77
Número:3
Página de inicio:642
Página de fin:660
DOI: http://dx.doi.org/10.1007/s00453-015-0095-6
Título revista:Algorithmica
Título revista abreviado:Algorithmica
ISSN:01784617
CODEN:ALGOE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01784617_v77_n3_p642_Lin

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Citas:

---------- APA ----------
Lin, M.C., Mizrahi, M.J. & Szwarcfiter, J.L. (2017) . Exact Algorithms for Minimum Weighted Dominating Induced Matching. Algorithmica, 77(3), 642-660.
http://dx.doi.org/10.1007/s00453-015-0095-6
---------- CHICAGO ----------
Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L. "Exact Algorithms for Minimum Weighted Dominating Induced Matching" . Algorithmica 77, no. 3 (2017) : 642-660.
http://dx.doi.org/10.1007/s00453-015-0095-6
---------- MLA ----------
Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L. "Exact Algorithms for Minimum Weighted Dominating Induced Matching" . Algorithmica, vol. 77, no. 3, 2017, pp. 642-660.
http://dx.doi.org/10.1007/s00453-015-0095-6
---------- VANCOUVER ----------
Lin, M.C., Mizrahi, M.J., Szwarcfiter, J.L. Exact Algorithms for Minimum Weighted Dominating Induced Matching. Algorithmica. 2017;77(3):642-660.
http://dx.doi.org/10.1007/s00453-015-0095-6