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Discrete & Computational Geometry

, Volume 28, Issue 4, pp 639–648 | Cite as

The k Most Frequent Distances in the Plane

  • Solymosi
  • Tardos
  • Tóth
Article

Abstract

A new upper bound is shown for the number of incidences between n points and n families of concentric circles in the plane. As a consequence, it is shown that the number of the k most frequent distances among n points in the plane is f n (k)=O(n 1.4571 k .6286 ) improving on an earlier bound of Akutsu, Tamaki, and Tokuyama.

Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  • Solymosi
    • 1
  • Tardos
    • 2
  • Tóth
    • 3
  1. 1.Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA solymosi@math.ucsd.edu USA
  2. 2.Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu Hungary
  3. 3.Institute for Theoretical Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland toth@inf.ethz.chSwitzerland

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