Hitting sets when the VC-dimension is small

Guy Even, Dror Rawitz, Shimon Shahar

Research output: Contribution to journalArticlepeer-review

Abstract

We present an approximation algorithm for the hitting set problem when the VC-dimension of the set system is small. Our algorithm uses a linear programming relaxation to compute a probability measure for which ε-nets are always hitting sets (see Corollary 15.6 in Pach and Agarwal [Combinatorial Geometry, J. Wiley, New York, 1995]). The comparable algorithm of Brönnimann and Goodrich [Almost optimal set covers in finite VC-dimension, Discrete Comput. Geom. 14 (1995) 463] computes such a probability measure by an iterative reweighting technique. The running time of our algorithm is comparable with theirs, and the approximation ratio is smaller by a constant factor. We also show how our algorithm can be parallelized and extended to the minimum cost hitting set problem.

Original languageEnglish
Pages (from-to)358-362
Number of pages5
JournalInformation Processing Letters
Volume95
Issue number2
DOIs
StatePublished - 31 Jul 2005

Keywords

  • Approximation algorithms
  • Computational geometry
  • Hitting set
  • VC-dimension

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