Sharp bounds on geometric permutations of pairwise disjoint balls in Rd

Shakhar Smorodinsky, Joseph S.B. Mitchell, Micha Sharir

Research output: Contribution to conferencePaperpeer-review

1 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. We show that the maximum number of geometric permutations of a sufficiently large collection of pair-wise disjoint unit discs in the plane is 2, improving the previous upper bound of 3 given in [5].

Original languageEnglish
Pages400-406
Number of pages7
DOIs
StatePublished - 1 Jan 1999
Externally publishedYes
EventProceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA
Duration: 13 Jun 199916 Jun 1999

Conference

ConferenceProceedings of the 1999 15th Annual Symposium on Computational Geometry
CityMiami Beach, FL, USA
Period13/06/9916/06/99

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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