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

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    Say that an edge of a graph GG dominates itself and every other edge adjacent to it. An edge dominating set of a graph G=(V,E)G=(V,E) is a subset of edges Eβ€²βŠ†EE' \subseteq E which dominates all edges of GG. In particular, if every edge of GG is dominated by exactly one edge of Eβ€²E' then Eβ€²E' 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 Oβˆ—(1.1939n)O^*(1.1939^n) time and polynomial (linear) space. This improves over any existing exact algorithm for the problems in consideration.Comment: 17 page
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