Exact Algorithms for Edge Domination

In this paper we present a faster exact exponential timealgorithm for the edge dominating set problem. Our algorithm usesO(1.3226n) time and polynomial space. The algorithm combines an enumerationapproach based on enumerating minimal vertex covers withthe branch and reduce paradigm. Its time bound is obtained using themeasure and conquer technique. The algorithm is obtained by startingwith a slower algorithm which is refined stepwise. In this way a series ofalgorithms appears, each one slightly faster than the previous, resultingin the O(1.3226n) time algorithm. The techniques also gives faster exact algorithms for: minimum weightedge dominating set, minimum (weight) maximal matching, matrix dominationand the parametrised version of minimum weight maximal matching.

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