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Discrete & Computational Geometry

, Volume 44, Issue 4, pp 883–895 | Cite as

Improved Results on Geometric Hitting Set Problems

  • Nabil H. Mustafa
  • Saurabh Ray
Article

Abstract

We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P = NP, it is not possible to get Fully Polynomial Time Approximation Algorithms (FPTAS) for such problems. We give the first PTAS for this problem when the geometric objects are half-spaces in ℝ3 and when they are an r-admissible set regions in the plane (this includes pseudo-disks as they are 2-admissible). Quite surprisingly, our algorithm is a very simple local-search algorithm which iterates over local improvements only.

Keywords

Hitting sets Local search Epsilon nets Greedy algorithms Transversals Approximation algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. of Computer ScienceLUMSLahorePakistan
  2. 2.Max-Plank-Institut für InformatikSaarbrückenGermany

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