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 c n 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.
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Fomin, F.V., Kratsch, D., Woeginger, G.J. (2004). Exact (Exponential) Algorithms for the Dominating Set Problem. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_21
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DOI: https://doi.org/10.1007/978-3-540-30559-0_21
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