Linear Kernel for Planar Connected Dominating Set

  • Daniel Lokshtanov
  • Matthias Mnich
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


We provide polynomial time data reduction rules for Connected Dominating Set in planar graphs and analyze these to obtain a linear kernel for the planar Connected Dominating Set problem. To obtain the desired kernel we introduce a method that we call reduce or refine. Our kernelization algorithm analyzes the input graph and either finds an appropriate reduction rule that can be applied, or zooms in on a region of the graph which is more amenable to reduction. We find this method of independent interest and believe that it will be useful to obtain linear kernels for other problems on planar graphs.


Planar Graph Vertex Cover Linear Kernel Kernel Size Reduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel Lokshtanov
    • 1
  • Matthias Mnich
    • 2
  • Saket Saurabh
    • 1
  1. 1.Institutt for InformatikkUniversitetet i BergenBergenNorway
  2. 2.Faculteit Wiskunde en InformaticaTechnische Universiteit EindhovenEindhovenThe Netherlands

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