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A (4 + ε)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs

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Approximation and Online Algorithms (WAOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5893))

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Abstract

We present a (4 + ε)-approximation algorithm for the problem of computing a minimum-weight dominating set in unit disk graphs, where ε is an arbitrarily small constant. The previous best known approximation ratio was 5 + ε. The main result of this paper is a 4-approximation algorithm for the problem restricted to constant-size areas. To obtain the (4 + ε)-approximation algorithm for the unrestricted problem, we then follow the general framework from previous constant-factor approximations for the problem: We consider the problem in constant-size areas, and combine the solutions obtained by our 4-approximation algorithm for the restricted case to get a feasible solution for the whole problem. Using the shifting technique (selecting a best solution from several considered partitionings of the problem into constant-size areas) we obtain the claimed (4 + ε)-approximation algorithm. By combining our algorithm with a known algorithm for node-weighted Steiner trees, we obtain a 7.875-approximation for the minimum-weight connected dominating set problem in unit disk graphs.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Leicester, England

    Thomas Erlebach

  2. Institute of Theoretical Computer Science, ETH Zurich, Switzerland

    Matúš Mihalák

Authors
  1. Thomas Erlebach
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  2. Matúš Mihalák
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Editors and Affiliations

  1. IBISC, CNRS FRE 3190, Université d’Evry Val d’Essonne, Place des Terasses, Tour Evry 2, 91000, Evry Cedex, France

    Evripidis Bampis

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

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Erlebach, T., Mihalák, M. (2010). A (4 + ε)-Approximation for the Minimum-Weight Dominating Set Problem in Unit Disk Graphs. In: Bampis, E., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2009. Lecture Notes in Computer Science, vol 5893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12450-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-12450-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12449-5

  • Online ISBN: 978-3-642-12450-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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