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Weakly Cooperative Guards in Grids

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Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3480))

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Abstract

We show that a minimum coverage of a grid of n segments has n–p 3 weakly cooperative guards, where p 3 is the size of the maximum P 3-matching in the intersection graph of the grid. This makes the minimum weakly cooperative guards problem in grids NP-hard, as we prove that the maximum P 3-matching problem in subcubic bipartite planar graphs is NP-hard. At last, we propose a 7/6-approximation algorithm for the minimum weakly cooperative guards problem.

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Author information

Authors and Affiliations

  1. Department of Algorithms and System Modeling, Gdańsk University of Technology, Poland

    Michał Małafiejski

  2. Institute of Mathematics, Gdańsk University, Poland

    Paweł Żyliński

Authors
  1. Michał Małafiejski
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  2. Paweł Żyliński
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, P.O. Box, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, P.O. Box, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Małafiejski, M., Żyliński, P. (2005). Weakly Cooperative Guards in Grids. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424758_68

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  • DOI: https://doi.org/10.1007/11424758_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25860-5

  • Online ISBN: 978-3-540-32043-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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