Paper Info
Title
Conflict-Free Coloring of Intersection Graphs of Geometric Objects.
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 conflict-free 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 ρ-fat objects in the plane.
Year
DOI
Venue
2018
10.5555/3174304.3175459
SODA '18: Symposium on Discrete Algorithms New Orleans Louisiana January, 2018
Keywords
Field
DocType
Conflict-free coloring, Geometric graphs, Pseudo-discs, Axis-parallel rectangles, List coloring
Discrete mathematics,Edge coloring,Complete coloring,Combinatorics,Fractional coloring,Chordal graph,List coloring,Brooks' theorem,Greedy coloring,Mathematics,Graph coloring
Conference
Volume
Issue
ISSN
64
3
0179-5376
ISBN
Citations 
PageRank 
978-1-61197-503-1
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Chaya Keller134.52
Shakhar Smorodinsky242243.47