Improved bounds for geometric permutations

Natan Rubin*, Haim Kaplan, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that the number of geometric permutations of an arbitrary collection of n pairwise disjoint convex sets in Rd, for d = 3, is O(n2d-3 log n), improving Wenger's 20-year-old bound of O(n2d-2).

Original languageEnglish
Pages (from-to)367-390
Number of pages24
JournalSIAM Journal on Computing
Issue number2
StatePublished - 2012


  • Combinatorial complexity
  • Convex sets
  • Geometric permutations
  • Line transversals
  • Lines in space


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