Improved Algorithms and Complexity Results for Power Domination in Graphs

  • Jiong Guo
  • Rolf Niedermeier
  • Daniel Raible
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3623)

Abstract

The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G=(V,E), find a minimum P ⊆ V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. We show that Power Dominating Set can be solved by “bounded-treewidth dynamic programs.” Moreover, we simplify and extend several NP-completeness results, particularly showing that Power Dominating Set remains NP-complete for planar graphs, for circle graphs, and for split graphs. Specifically, our improved reductions imply that Power Dominating Set parameterized by |P| is W[2]-hard and cannot be better approximated than Dominating Set.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jiong Guo
    • 1
  • Rolf Niedermeier
    • 1
  • Daniel Raible
    • 2
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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