Upper bound on the number of planar k-sets

Janos Pach, William Steiger, Endre Szemeredi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

Given a set S of n points, a subset X of size k is called a k-set if there is a hyperplane II that separates X from Xc. It is proved that O(n√k/log*k) is an upper bound for the number of k-sets in the plane, thus improving the previous bound of P. Erdos et al. (A Survey of Combinatorial Theory, North-Holland, 1973, pp. 139-149) by a factor of log*k. The method can be extended to give the bound O(n√k/(log k)ε). The proof only establishes the weaker result; it uses the geometry and combinatorics together in a stronger way than in the earlier work.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherPubl by IEEE
Pages72-79
Number of pages8
ISBN (Print)0818619821
Publication statusPublished - Nov 1 1989
Event30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA
Duration: Oct 30 1989Nov 1 1989

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

Other

Other30th Annual Symposium on Foundations of Computer Science
CityResearch Triangle Park, NC, USA
Period10/30/8911/1/89

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ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Pach, J., Steiger, W., & Szemeredi, E. (1989). Upper bound on the number of planar k-sets. In Annual Symposium on Foundations of Computer Science (Proceedings) (pp. 72-79). (Annual Symposium on Foundations of Computer Science (Proceedings)). Publ by IEEE.