## Abstract

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n^{8} log n) and O(n^{15} log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio (1+1/k)^{2} in n^{O(k)} time.

Original language | English |
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Pages (from-to) | 461-477 |

Number of pages | 17 |

Journal | International Journal of Computational Geometry and Applications |

Volume | 23 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jan 2013 |

## Keywords

- Piercing
- approximation algorithm
- minimum dominating set
- unit disk

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics