Exact (exponential) algorithms for the dominating set problem

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 eta of vertices. The contribution of this paper are 'nice' exponential time complexities that are bounded by functions of the form c(eta) with reasonably small constants c < 2: For arbitrary graphs we get a time complexity of 1.93782(eta). And for the special cases of split graphs, bipartite graphs, and graphs of maximum degree three, we reach time complexities of 1.41422(eta), 1.732061(eta), and 1.51433(eta), respectively.