Geometric spanners with small chromatic number

Prosenjit Bose, Paz Carmi, Mathieu Couture, Anil Maheshwari, Michiel Smid, Norbert Zeh

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

1 Scopus citations

Abstract

Given an integer k ≥ 2, we consider the problem of computing the smallest real number t(k) such that for each set P of points in the plane, there exists a t(k)-spanner for P that has chromatic number at most k. We prove that t(2)∈=∈3, t(3)∈=∈2, , and give upper and lower bounds on t(k) for k∈>∈4. We also show that for any ε>∈0, there exists a (1∈+∈ε)t(k)-spanner for P that has O(|P|) edges and chromatic number at most k. Finally, we consider an on-line variant of the problem where the points of P are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that t(2)∈=∈3, , , and give upper and lower bounds on t(k) for k∈>∈4.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 5th International Workshop, WAOA 2007, Revised Papers
Pages75-88
Number of pages14
DOIs
StatePublished - 27 Aug 2008
Externally publishedYes
Event5th International Workshop on Approximation and Online Algorithms, WAOA 2007 - Eilat, Israel
Duration: 11 Oct 200712 Oct 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4927 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Workshop on Approximation and Online Algorithms, WAOA 2007
Country/TerritoryIsrael
CityEilat
Period11/10/0712/10/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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