Selecting points that are heavily covered by pseudo-circles, spheres or rectangles

Shakhar Smorodinsky, Micha Sharir

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper we prove several point selection theorems concerning objects 'spanned' by a finite set of points. For example, we show that for any set P of n points in ℝ2 and any set C of m ≥4n distinct pseudo-circles, each passing through a distinct pair of points of P, there is a point in P that is covered by (i.e., lies in the interior of) Ω(m 2/n2) pseudo-circles of C. Similar problems involving point sets in higher dimensions are also studied. Most of our bounds are asymptotically tight, and they improve and generalize results of Chazelle, Edelsbrunner, Guibas, Hershberger, Seidel and Sharir, where weaker bounds for some of these cases were obtained.

Original languageEnglish
Pages (from-to)389-411
Number of pages23
JournalCombinatorics Probability and Computing
Issue number3
StatePublished - 1 May 2004
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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