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Approximation of geometric dispersion problems

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Book cover Approximation Algorithms for Combinatiorial Optimization (APPROX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1444))

Abstract

We consider problems of distributing a number of points within a connected polygonal domain P, such that the points are “far away” from each other. Problems of this type have been considered before for the case where the possible locations form a discrete set. Dispersion problems are closely related to packing problems. While Hochbaum and Maass (1985) have given a polynomial time approximation scheme for packing, we show that geometric dispersion problems cannot be approximated arbitrarily well in polynomial time, unless P=NP. We give a 2/3 approximation algorithm for one version of the geometric dispersion problem. This algorithm is strongly polynomial in the size of the input, i.e., its running time does not depend on the area of P. We also discuss extensions and open problems.

This work was supported by the German Federal Ministry of Education, Science, Research and Technology (BMBF, Förderkennzeichen 01 IR 411 C7).

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  1. Center for Parallel Computing, UniversitÄt zu Köln, D-50923, Köln, Germany

    Christoph Baur & Sándor P. Fekete

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  1. Christoph Baur
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  2. Sándor P. Fekete
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Klaus Jansen José Rolim

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© 1998 Springer-Verlag Berlin Heidelberg

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Baur, C., Fekete, S.P. (1998). Approximation of geometric dispersion problems. In: Jansen, K., Rolim, J. (eds) Approximation Algorithms for Combinatiorial Optimization. APPROX 1998. Lecture Notes in Computer Science, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053964

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  • DOI: https://doi.org/10.1007/BFb0053964

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  • Print ISBN: 978-3-540-64736-2

  • Online ISBN: 978-3-540-69067-2

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