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 n of vertices. The contribution of this paper are ‘nice’ exponential time complexities that are bounded by functions of the form c n with reasonably small constants c<2: For arbitrary graphs we get a time complexity of 1.93782 n . And for the special cases of split graphs, bipartite graphs, and graphs of maximum degree three, we reach time complexities of 1.41422 n , 1.73206 n , and 1.51433 n , respectively.
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