Coloring geometric range spaces

Greg Aloupis, Jean Cardinal, Sébastien Collette, Stefan Langerman, Shakhar Smorodinsky

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

6 Scopus citations

Abstract

Given a set of points in or , we aim to color them such that every region of a certain family (for instance disks) containing at least a certain number of points contains points of many different colors. Using k colors, it is not always possible to ensure that every region containing k points contains all k colors. Thus, we introduce two relaxations: either we allow the number of colors to increase to c(k), or we require that the number of points in each region increases to p(k). We give upper bounds on c(k) and p(k) for halfspaces, disks, and pseudo-disks. We also consider the dual question, where we want to color regions instead of points. This is related to previous results of Pach, Tardos and Tóth on decompositions of coverings.

Original languageEnglish
Title of host publicationLATIN 2008
Subtitle of host publicationTheoretical Informatics - 8th Latin American Symposium, Proceedings
Pages146-157
Number of pages12
DOIs
StatePublished - 12 May 2008
Externally publishedYes
Event8th Latin American TheoreticalINformatics Symposium, LATIN 2008 - Buzios, Brazil
Duration: 7 Apr 200811 Apr 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4957 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th Latin American TheoreticalINformatics Symposium, LATIN 2008
Country/TerritoryBrazil
CityBuzios
Period7/04/0811/04/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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