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Approximation of geometric dispersion problems

Extended abstract
  • Christoph Baur
  • Sándor P. Fekete
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Approximation Scheme Knapsack Problem Binary Search Approximation Factor Simple Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Christoph Baur
    • 1
  • Sándor P. Fekete
    • 1
  1. 1.Center for Parallel ComputingUniversitÄt zu KölnKölnGermany

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