An Exact 2.9416n Algorithm for the Three Domatic Number Problem

  • Tobias Riege
  • Jörg Rothe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


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 3 n , up to polynomial factors. In this paper, we design an exact deterministic algorithm for this problem running in time 2.9416 n . 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.


Exact algorithms domatic number problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tobias Riege
    • 1
  • Jörg Rothe
    • 1
  1. 1.Institut für InformatikHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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