Sharp bounds on geometric permutations of pairwise disjoint balls in ℝd

S. Smorodinsky, J. S.B. Mitchell, M. Sharir

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in ℝd, is Θ(nd-1). This improves substantially the upper bound of O(n2d-2) known for general convex sets [9]. We show that the maximum number of geometric permutations of a sufficiently large collection of pairwise disjoint unit disks in the plane is two, improving the previous upper bound of three given in [5].

Original languageEnglish
Pages (from-to)247-259
Number of pages13
JournalDiscrete and Computational Geometry
Volume23
Issue number2
DOIs
StatePublished - 1 Jan 2000
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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