Conflict-free coloring of unit disks

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.