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Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs

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Book cover Parameterized and Exact Computation (IPEC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7112))

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Abstract

We present a linear-time kernelization algorithm that transforms a given planar graph G with domination number γ(G) into a planar graph G′ of size O(γ(G)) with γ(G) = γ(G′). In addition, a minimum dominating set for G can be inferred from a minimum dominating set for G′. In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time. This improves on previous kernelization algorithms that provide linear-size kernels in cubic time.

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Authors and Affiliations

  1. Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    René van Bevern, Sepp Hartung, Rolf Niedermeier & Mathias Weller

  2. Institut für Informatik, Universität Augsburg, Augsburg, Germany

    Frank Kammer

Authors
  1. René van Bevern
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  2. Sepp Hartung
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  3. Frank Kammer
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  4. Rolf Niedermeier
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  5. Mathias Weller
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Editor information

Editors and Affiliations

  1. MTA SZTAKI, Lágymányosi u. 11, 1111, Budapest, Hungary

    Dániel Marx

  2. Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraße 55, 52056, Aachen, Germany

    Peter Rossmanith

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van Bevern, R., Hartung, S., Kammer, F., Niedermeier, R., Weller, M. (2012). Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-28050-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28049-8

  • Online ISBN: 978-3-642-28050-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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