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: | , , |
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| Formato: | SER |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03029743_v8283LNCS_n_p558_Lin |
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| Sumario: | 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. |
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