Conflict-free coloring of unit disks Original Research Article

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 image in the total coverage area, there exist a color image and a region image such that image, the region image is colored image, and every other region image that contains image is not colored image. 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 image approximation algorithm for the conflict-free coloring problem where the regions are unit disks.