A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set

A dominating set of a graph G = (V,E) is a subset of vertices such that every vertex in has at least one neighbour in . Moreover if is an independent set, i.e. no vertices in are pairwise adjacent, then is said to be an independent dominating set. Finding a minimum independent dominating set in a graph is an NP-hard problem. We give an algorithm computing a minimum independent dominating set of a graph on n vertices in time O(1.3575n). Furthermore, we show that Ω(1.3247n) is a lower bound on the worst-case running time of this algorithm.

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