Abstract
The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no polynomial-time algorithm is known for it. The naive deterministic algorithm for this problem runs in time 3n, up to polynomial factors. In this paper, we design an exact deterministic algorithm for this problem running in time 2.9416n. Thus, our algorithm can handle problem instances of larger size than the naive algorithm in the same amount of time. We also present another deterministic and a randomized algorithm for this problem that both have an even better performance for graphs with small maximum degree.
Work supported in part by the DFG under Grant RO 1202/9-1.
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Riege, T., Rothe, J. (2005). An Exact 2.9416n Algorithm for the Three Domatic Number Problem. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_63
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DOI: https://doi.org/10.1007/11549345_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28702-5
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