TY - JOUR

T1 - Hitting sets when the VC-dimension is small

AU - Even, Guy

AU - Rawitz, Dror

AU - Shahar, Shimon

PY - 2005/7/31

Y1 - 2005/7/31

N2 - 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.

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.

KW - Approximation algorithms

KW - Computational geometry

KW - Hitting set

KW - VC-dimension

UR - http://www.scopus.com/inward/record.url?scp=20444474622&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2005.03.010

DO - 10.1016/j.ipl.2005.03.010

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AN - SCOPUS:20444474622

SN - 0020-0190

VL - 95

SP - 358

EP - 362

JO - Information Processing Letters

JF - Information Processing Letters

IS - 2

ER -