Discrete & Computational Geometry

, Volume 26, Issue 2, pp 195–204

An Improved Bound for k-Sets in Three Dimensions

  • M. Sharir
  • S. Smorodinsky
  • G. Tardos
Article

DOI: 10.1007/s00454-001-0005-3

Cite this article as:
Sharir, M., Smorodinsky, S. & Tardos, G. Discrete Comput Geom (2001) 26: 195. doi:10.1007/s00454-001-0005-3

Abstract

We prove that the maximum number of k -sets in a set S of n points in \Bbb R 3 is O(nk3/2) . This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • M. Sharir
    • 1
  • S. Smorodinsky
    • 1
  • G. Tardos
    • 3
  1. 1.School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel \{sharir, shakhar\}@math.tau.ac.il Israel
  2. 2.Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA USA
  3. 3.Rényi Institute of the Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.huHungary