Conict-free coloring of intersection graphs of geometric objects

Chaya Keller, Shakhar Smorodinsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

In FOCS'2002, Even et al. introduced and studied the notion of conflict-free colorings of geometrically defined hypergraphs. They motivated it by frequency assignment problems in cellular networks. This notion has been extensively studied since then. A conflict-free coloring of a graph is a coloring of its vertices such that the neighborhood (pointed or closed) of each vertex contains a vertex whose color differs from the colors of all other vertices in that neighborhood. In this paper we study conflictfree colorings of intersection graphs of geometric objects. We show that any intersection graph of n pseudo-discs in the plane admits a conflict-free coloring with O(log n) colors, with respect to both closed and pointed neighborhoods. We also show that the latter bound is asymptotically sharp. Using our methods, we obtain the following strengthening of the two main results of Even et al.: Any family F of n discs in the plane can be colored with O(log n) colors in such a way that for any disc B in the plane, the set of discs in F that intersect B contains a uniquely-colored element. Moreover, such a coloring can be computed deterministically in polynomial time. In view of the original motivation to study such colorings, this strengthening suggests further applications to frequency assignment in wireless networks. Finally, we present bounds on the number of colors needed for conflict-free colorings of other classes of intersection graphs, including intersection graphs of axis-parallel rectangles and of ?-fat objects in the plane.

Original languageEnglish
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Pages2397-2411
Number of pages15
ISBN (Electronic)9781611975031
DOIs
StatePublished - 1 Jan 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: 7 Jan 201810 Jan 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Country/TerritoryUnited States
CityNew Orleans
Period7/01/1810/01/18

ASJC Scopus subject areas

  • Software
  • Mathematics (all)

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