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International Conference on Computational Science and Its Applications

ICCSA 2004: Computational Science and Its Applications – ICCSA 2004 pp 137–146Cite as

On the Time Complexity of Rectangular Covering Problems in the Discrete Plane

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3045))

Abstract

This paper addresses the computational complexity of optimization problems dealing with the covering of points in the discrete plane by rectangles. Particularly we prove the NP-hardness of such a problem(class) defined by the following objective function: Simultaneously minimize the total area, the total circumference and the number of rectangles used for covering (where the length of every rectangle side is required to lie in a given interval). By using a tiling argument we also prove that a variant of this problem, fixing only the minimal side length of rectangles, is NP-hard. Such problems may appear at the core of applications like data compression, image processing or numerically solving partial differential equations by multigrid computations.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, D-50969, Köln, Germany

    Stefan Porschen

Authors
  1. Stefan Porschen
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  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. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

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

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Porschen, S. (2004). On the Time Complexity of Rectangular Covering Problems in the Discrete Plane. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_15

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  • DOI: https://doi.org/10.1007/978-3-540-24767-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22057-2

  • Online ISBN: 978-3-540-24767-8

  • eBook Packages: Springer Book Archive

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