Improved bound for k-sets in three dimensions

Micha Sharir, Shakhar Smorodinsky, Gabor Tardos

Research output: Contribution to conferencePaperpeer-review

9 Scopus citations


The problem of determining tight asymptotic bounds on the maximum number of k-sets is one of the most challenging open problems in combinatorial geometry. It is a widely studied problem due to its importance in analyzing geometric algorithms. The maximum number of k-sets in a set of n points in three dimensions is proven O(nk3/2). This improves substantially the best known upper bound of O(nk5/3).

Original languageEnglish
Number of pages7
StatePublished - 1 Jan 2000
Externally publishedYes
Event16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong
Duration: 12 Jun 200014 Jun 2000


Conference16th Annual Symposium on Computational Geometry
CityHong Kong, Hong Kong

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


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