Conflict-free coloring of unit disks

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 pp in the total coverage area, there exist a color ii and a region DD such that p∈Dp∈D, the region DD is colored ii, and every other region D′D′ that contains pp is not colored ii. 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)O(1) approximation algorithm for the conflict-free coloring problem where the regions are unit disks.