## Abstract

We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P = NP, it is not possible to get Fully Polynomial Time Approximation Algorithms (FPTAS) for such problems. We give the first PTAS for this problem when the geometric objects are half-spaces in ℝ^{3} and when they are an r-admissible set regions in the plane (this includes pseudo-disks as they are 2-admissible). Quite surprisingly, our algorithm is a very simple local-search algorithm which iterates over local improvements only.

Original language | English (US) |
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Pages (from-to) | 883-895 |

Number of pages | 13 |

Journal | Discrete and Computational Geometry |

Volume | 44 |

Issue number | 4 |

DOIs | |

State | Published - 2010 |

## Keywords

- Approximation algorithms
- Epsilon nets
- Greedy algorithms
- Hitting sets
- Local search
- Transversals

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics