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.
CITATION STYLE
Lin, M. C., Mizrahi, M. J., & Szwarcfiter, J. L. (2013). An O*(1.1939n) time algorithm for minimum weighted dominating induced matching. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8283 LNCS, pp. 558–567). https://doi.org/10.1007/978-3-642-45030-3_52
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