Efficient Data Reduction for Dominating Set: A Linear Problem Kernel for the Planar Case

  • Jochen Alber
  • Michael R. Fellows
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2368)


Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set on planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy to implement reduction rules. This answers an open question from previous work on the parameterized complexity of Dominating Set on planar graphs.


Planar Graph Vertex Cover Tree Decomposition Single Vertex Reduction Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jochen Alber
    • 1
  • Michael R. Fellows
    • 2
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany
  2. 2.School of Electrical Engineering and Computer ScienceUniversity of NewcastleCallaghanAustralia

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