On neighbors in geometric permutations

Micha Sharir, Shakhar Smorodinsky

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We introduce a new notion of 'neighbors' in geometric permutations. We conjecture that the maximum number of neighbors in a set S of n pairwise disjoint convex bodies in R(d) is O(n), and we prove this conjecture for d=2. We show that if the set of pairs of neighbors in a set S is of size N, then S admits at most O(N d-1) geometric permutations. Hence, we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any finite family of pairwise disjoint convex bodies in the plane.

Original languageEnglish
Pages (from-to)327-335
Number of pages9
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 6 Jul 2003
Externally publishedYes


  • Geometric permutations
  • Line transversals

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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