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Exact (Exponential) Algorithms for the Dominating Set Problem

  • Fedor V. Fomin
  • Dieter Kratsch
  • Gerhard J. Woeginger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3353)

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 1.93782 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Dieter Kratsch
    • 2
  • Gerhard J. Woeginger
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LITAUniversité de MetzMetz Cedex 01France
  3. 3.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands

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