Algorithms pp 419-428

A hyperplane Incidence problem with applications to counting distances

  • Herbert Edelsbrunner
  • Micha Sharir
Conference paper

DOI: 10.1007/3-540-52921-7_91

Part of the Lecture Notes in Computer Science book series (LNCS, volume 450)
Cite this paper as:
Edelsbrunner H., Sharir M. (1990) A hyperplane Incidence problem with applications to counting distances. In: Asano T., Ibaraki T., Imai H., Nishizeki T. (eds) Algorithms. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg

Abstract

This paper proves an O(m2/3n2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Herbert Edelsbrunner
    • 1
  • Micha Sharir
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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