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Fixed Parameter Algorithms for Planar Dominating Set and Related Problems

  • Jochen Alber
  • Hans L. Bodlaender
  • Henning Fernau
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1851)

Abstract

We present an algorithm for computing the domination number of a planar graph that uses \( O\left( {c^{\sqrt k } n} \right) \) time, where k is the domination number of the given planar input graph and \( c = 3^{6\sqrt {34} } \) . To obtain this result, we show that the treewidth of a planar graph with domination number k is \( O\left( {\sqrt k } \right) \) , and that such a tree decomposition can be found in \( O\left( {\sqrt {kn} } \right) \) time. The same technique can be used to show that the disk dimension problem (find a minimum set of faces that cover all vertices of a given plane graph) can be solved in \( O\left( {c_1^{\sqrt {k_n } } } \right) \) time for \( c_1 = 2^{6\sqrt {34} } \) . Similar results can be obtained for some variants of {updominating set}, e.g., INDEPENDENT DOMINATING SET.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jochen Alber
    • 1
  • Hans L. Bodlaender
    • 2
  • Henning Fernau
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.WSI für Informatik, Sand 13Universität TübingenTübingenFed. Rep. of Germany
  2. 2.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

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