Optimal cover of points by disksin a simple polygon

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let P be a simple polygon, and let Q be a set of points in P. We present an almostlinear time algorithm for computing a minimum cover of Q by disks that are contained in P. We then generalize the algorithm so that it can compute a minimum cover of Q by homothets of any fixed compact convex set O of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [Lecture Notes in Comput. Sci. 5664, 2009, pp. 447-458]. We also consider the minimum disk-cover problem when Q is contained in a (sufficiently narrow) annulus and present a nearly linear algorithm for this case, too.

Original languageEnglish
Pages (from-to)1647-1661
Number of pages15
JournalSIAM Journal on Computing
Issue number6
StatePublished - 1 Dec 2011


  • Chordal graphs
  • Geometric covering
  • Minimum disk cover

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


Dive into the research topics of 'Optimal cover of points by disksin a simple polygon'. Together they form a unique fingerprint.

Cite this