Optimal cover of points by disks in a simple polygon

Haim Kaplan, Matthew J. Katz, Gila Morgenstern, Micha Sharir

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

3 Scopus citations

Abstract

Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2010 - 18th Annual European Symposium, Proceedings
Pages475-486
Number of pages12
EditionPART 1
DOIs
StatePublished - 19 Nov 2010
Event18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom
Duration: 6 Sep 20108 Sep 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6346 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th Annual European Symposium on Algorithms, ESA 2010
Country/TerritoryUnited Kingdom
CityLiverpool
Period6/09/108/09/10

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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