Hitting sets when the VC-dimension is small

Guy Even; Dror Rawitz; Shimon Shahar

doi:10.1016/j.ipl.2005.03.010

Hitting sets when the VC-dimension is small

Guy Even, Dror Rawitz, Shimon Shahar

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

95 Scopus citations

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 language	English
Pages (from-to)	358-362
Number of pages	5
Journal	Information Processing Letters
Volume	95
Issue number	2
DOIs	https://doi.org/10.1016/j.ipl.2005.03.010
State	Published - 31 Jul 2005
Externally published	Yes

Keywords

Approximation algorithms
Computational geometry
Hitting set
VC-dimension

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10.1016/j.ipl.2005.03.010

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AB - 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.

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Hitting sets when the VC-dimension is small

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Keywords

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