## Abstract

The paper considers the geometric conflict-free coloring problem, introduced in [G. Even, Z. Lotker, D. Ron, S. Smorodinsky, Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks, SIAM J. Comput. 33 (2003) 94-133]. The input of this problem is a set of regions in the plane and the output is an assignment of colors to the regions, such that for every point p in the total coverage area, there exist a color i and a region D such that p ∈ D, the region D is colored i, and every other region D^{′} that contains p is not colored i. The target is to minimize the number of colors used. This problem arises from issues of frequency assignment in radio networks. The paper presents an O (1) approximation algorithm for the conflict-free coloring problem where the regions are unit disks.

Original language | English |
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Pages (from-to) | 1521-1532 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 7 |

DOIs | |

State | Published - 6 Apr 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:This research was supported in part by grants from the Minerva Foundation and the Israel Ministry of Industry and Commerce.

## Keywords

- Conflict-free coloring
- Unit disk graphs
- Wireless networks