### 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) |
---|---|

Pages (from-to) | 25-32 |

Number of pages | 8 |

Journal | Discrete Applied Mathematics |

Volume | 240 |

DOIs | |

State | Published - May 11 2018 |

### Fingerprint

### Keywords

- Approximation algorithms
- Computational geometry
- Geometric hitting sets

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

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

**Practical and efficient algorithms for the geometric hitting set problem.** / Bus, Norbert; Mustafa, Nabil H.; Ray, Saurabh.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 240, pp. 25-32. https://doi.org/10.1016/j.dam.2017.12.018

}

TY - JOUR

T1 - Practical and efficient algorithms for the geometric hitting set problem

AU - Bus, Norbert

AU - Mustafa, Nabil H.

AU - Ray, Saurabh

PY - 2018/5/11

Y1 - 2018/5/11

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Computational geometry

KW - Geometric hitting sets

UR - http://www.scopus.com/inward/record.url?scp=85040735765&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040735765&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2017.12.018

DO - 10.1016/j.dam.2017.12.018

M3 - Article

VL - 240

SP - 25

EP - 32

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -