Abstract
Minimum Dominating Set is among the most studied classical NP-hard problems. On general graphs, an O(1.4864n) exact algorithm for this problem is known. Minimum Dominating Set remains NP-hard on chordal graphs where the current asymptotically-fastest exact algorithm solves the problem in O(1.3687n) time and super-polynomial space. In this paper, a simple exact polynomial-space algorithm that exploits the local structure of neighborhoods of simplicial vertices in chordal graphs is presented, resulting in an improved running time in O(1.3384n).
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