Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm

  • Francisco Claude
  • Reza Dorrigiv
  • Stephane Durocher
  • Robert Fraser
  • Alejandro López-Ortiz
  • Alejandro Salinger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)


Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem.


Unit Disk Simplification Rule Disk Centre Minimum Cardinality Unit Disk Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francisco Claude
    • 1
  • Reza Dorrigiv
    • 1
  • Stephane Durocher
    • 2
  • Robert Fraser
    • 1
  • Alejandro López-Ortiz
    • 1
  • Alejandro Salinger
    • 1
  1. 1.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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