## Abstract

In this article, we study approximation algorithms for the problem of computing minimum dominating set for a given set S of n unit disks in R^{2}. We first present a simple O(nlogk) time 5-factor approximation algorithm for this problem, where k is the size of the output. The best known 4-factor and 3-factor approximation algorithms for the same problem run in time O(n8logn) and O(n15logn) respectively [M. De, G. K. Das, P. Carmi and S. C. Nandy, Approximation algorithms for a variant of discrete piercing set problem for unit disks, Int. J. of Computational Geometry and Appl., 22(6):461-477, 2013]. We show that the time complexity of the in-place 4-factor approximation algorithm for this problem can be improved to O(n6logn). A minor modification of this algorithm produces a 143-factor approximation algorithm in O(n5logn) time. The same techniques can be applied to have a 3-factor and a 4513-factor approximation algorithms in time O(n11logn) and O(n10logn) respectively. Finally, we propose a very important shifting lemma, which is of independent interest, and it helps to present 52-factor approximation algorithm for the same problem. It also helps to improve the time complexity of the proposed PTAS for the problem.

Original language | English |
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Pages (from-to) | 227-244 |

Number of pages | 18 |

Journal | International Journal of Computational Geometry and Applications |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - 1 Sep 2015 |

## Keywords

- Minimum dominating set
- approximation algorithm
- unit disk graph

## ASJC Scopus subject areas

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