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

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Algorithm Theory — SWAT 2002 (SWAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2368))

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Abstract

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.

Work supported by the Deutsche Forschungsgemeinschaft (DFG), research project PEAL (Parameterized complexity and Exact ALgorithms), NI 369/1-1,1-2.

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Fed. Rep. of Germany

    Jochen Alber & Rolf Niedermeier

  2. School of Electrical Engineering and Computer Science, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia

    Michael R. Fellows

Authors
  1. Jochen Alber
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  2. Michael R. Fellows
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  3. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Kuopio, P.O. Box 1627, 70211, Kuopio, Finland

    Martti Penttonen

  2. BRICS, University of Aarhus, Department of Computer Science, NY Munkegade, 8000, Aarhus C, Denmark

    Erik Meineche Schmidt

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© 2002 Springer-Verlag Berlin Heidelberg

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Alber, J., Fellows, M.R., Niedermeier, R. (2002). Efficient Data Reduction for Dominating Set: A Linear Problem Kernel for the Planar Case. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_16

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  • DOI: https://doi.org/10.1007/3-540-45471-3_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43866-3

  • Online ISBN: 978-3-540-45471-7

  • eBook Packages: Springer Book Archive

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