An O *(1.1939 n ) Time Algorithm for Minimum Weighted Dominating Induced Matching
نویسندگان
چکیده
Say that an edge of a graph G dominates itself and every other edge adjacent to 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∗(1.1939n) time and polynomial (linear) space. This improves over any existing exact algorithm for the problems in consideration.
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