Exact (Exponential) algorithms for the dominating set problem

Abstract

We design fast exact algorithms for the problem of computing a minimum dominating set in undirected graphs. Since this problem is NP-hard, it comes with no big surprise that all our time complexities are exponential in the number n of vertices. The contribution of this paper are 'nice' exponential time complexities that are bounded by functions of the form cn with reasonably small constants c < 2: For arbitrary graphs we get a time complexity of 1.93782n. And for the special cases of split graphs, bipartite graphs, and graphs of maximum degree three, we reach time complexities of 1.41422n, 1.73206n, and 1.51433n, respectively. © Springer-Verlag 2004.