A Polynomial-Time Approximation Algorithm for a Geometric Dispersion Problem

  • Marc Benkert
  • Joachim Gudmundsson
  • Christian Knauer
  • Esther Moet
  • René van Oostrum
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We consider the problem of placing a maximal number of disks in a rectangular region containing obstacles such that no two disks intersect. Let α be a fixed real in (0,1]. We are given a bounding rectangle P and a set \(\cal{R}\) of possibly intersecting unit disks whose centers lie in P. The task is to pack a set \(\cal{B}\) of m disjoint disks of radius α into P such that no disk in \(\cal{B}\) intersects a disk in \(\cal{R}\), where m is the maximum number of unit disks that can be packed. Baur and Fekete showed that the problem cannot be solved in polynomial time for α≥13/14, unless \({\cal P}={\cal NP}\). In this paper we present an algorithm for α= 2/3.


Polynomial Time Unit Disk Pairwise Disjoint Original Optimization Problem Equal Circle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marc Benkert
    • 1
  • Joachim Gudmundsson
    • 2
  • Christian Knauer
    • 3
  • Esther Moet
    • 4
  • René van Oostrum
    • 4
  • Alexander Wolff
    • 1
  1. 1.Faculty of Computer ScienceKarlsruhe UniversityKarlsruheGermany
  2. 2.National ICT Australia LtdSydneyAustralia
  3. 3.Institute of Computer ScienceFreie Universität BerlinGermany
  4. 4.Department of Computing and Information SciencesUniversiteit UtrechtThe Netherlands

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