The potential to improve the choice: List conflict-free coloring for geometric hypergraphs

Panagiotis Cheilaris, Shakhar Smorodinsky, Marek Sulovský

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

6 Scopus citations

Abstract

Given a geometric hypergraph (or a range-space) H = (V; E), a coloring of its vertices is said to be conict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The study of this notion is motivated by frequency assignment problems in wireless networks. We study the list-coloring (or choice) version of this notion. In this version, each vertex is associated with a set of (admissible) colors and it is allowed to be colored only with colors from its set. List coloring arises naturally in the context of wireless networks. Our main result is a list coloring algorithm based on anew potential method. The algorithm produces a stronger unique-maximum coloring, in which colors are positive integers and the maximum color in every hyperedge occurs uniquely. As a corollary, we provide asymptotically sharp bounds on the size of the lists required to assure the existence of such unique-maximum colorings for many geometric hypergraphs (e.g., discs or pseudo-discs in the plane or points with respect to discs). Moreover, we provide an algorithm, such that, given a family of lists with the appropriate sizes, computes such a coloring from these lists.

Original languageEnglish
Title of host publicationProceedings of the 27th Annual Symposium on Computational Geometry, SCG'11
Pages424-432
Number of pages9
DOIs
StatePublished - 15 Jul 2011
Event27th Annual ACM Symposium on Computational Geometry, SCG'11 - Paris, France
Duration: 13 Jun 201115 Jun 2011

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference27th Annual ACM Symposium on Computational Geometry, SCG'11
Country/TerritoryFrance
CityParis
Period13/06/1115/06/11

Keywords

  • Algorithms
  • Theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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