Conflict-free coloring for rectangle ranges using O(n.382) colors

Deepak Ajwani, Khaled Elbassioni, Sathish Govindarajan, Saurabh Ray

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a set of points P R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with (nΒ+) colors in expected polynomial time, for any arbitrarily small > 0 and Β = 3?5<over>2 < 0.382. This improves upon the previously known bound of O(nlog log n/ log n).

Original languageEnglish (US)
Title of host publicationSPAA'07
Subtitle of host publicationProceedings of the Nineteenth Annual Symposium on Parallelism in Algorithms and Architectures
Pages181-187
Number of pages7
DOIs
StatePublished - 2007
EventSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures - San Diego, CA, United States
Duration: Jun 9 2007Jun 11 2007

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Other

OtherSPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures
CountryUnited States
CitySan Diego, CA
Period6/9/076/11/07

Keywords

  • Axis-parallel rectangles
  • Conflict-free coloring
  • Dominating sets
  • Frequency assignment in wireless networks
  • Monotone sequences

ASJC Scopus subject areas

  • Engineering(all)

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