### 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.

Original language | English (US) |
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Pages (from-to) | 25-32 |

Number of pages | 8 |

Journal | Discrete Applied Mathematics |

Volume | 240 |

DOIs | |

State | Published - May 11 2018 |

### Keywords

- Approximation algorithms
- Computational geometry
- Geometric hitting sets

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

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## Cite this

*Discrete Applied Mathematics*,

*240*, 25-32. https://doi.org/10.1016/j.dam.2017.12.018