Conflict-free coloring of unit disks

Nissan Lev-Tov, David Peleg

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish
Pages (from-to)1521-1532
Number of pages12
JournalDiscrete Applied Mathematics
Issue number7
StatePublished - 6 Apr 2009
Externally publishedYes

Bibliographical note

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


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


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