# Practical and efficient algorithms for the geometric hitting set problem

Practical and efficient algorithms for the geometric hitting set problem The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D . Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Applied Mathematics Elsevier

# Practical and efficient algorithms for the geometric hitting set problem

, Volume 240 – May 11, 2018
8 pages

/lp/elsevier/practical-and-efficient-algorithms-for-the-geometric-hitting-set-WhzNiF8oBa
Publisher
Elsevier
ISSN
0166-218X
D.O.I.
10.1016/j.dam.2017.12.018
Publisher site
See Article on Publisher Site

### Abstract

The geometric hitting set problem is one of the basic geometric combinatorial optimization problems: given a set P of points and a set D of geometric objects in the plane, the goal is to compute a small-sized subset of P that hits all objects in D . Recently Agarwal and Pan (2014) presented a near-linear time algorithm for the case where D consists of disks in the plane. The algorithm uses sophisticated geometric tools and data structures with large resulting constants. In this paper, we design a hitting-set algorithm for this case without the use of these data-structures, and present experimental evidence that our new algorithm has near-linear running time in practice, and computes hitting sets within 1.3-factor of the optimal hitting set. We further present dnet, a public source-code module that incorporates this improvement, enabling fast and efficient computation of small-sized hitting sets in practice.

### Journal

Discrete Applied MathematicsElsevier

Published: May 11, 2018

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