Advertisement

A sweep algorithm for the all-nearest-neighbors problem

  • Klaus Hinrichs
  • Jurg Nievergelt
  • Peter Schorn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 333)

Abstract

The 2-dimensional all-nearest-neighbors problem is solved directly in asymptotically optimal time O(n*log n) using a simple plane-sweep algorithm. We present the algorithm, its analysis, and a "foolproof" implementation which guarantees an exact result at the cost of using five-fold-precision rational arithmetic.

Keywords

Computational geometry complexity proximity problems plane-sweep algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [F 86]
    S. Fortune: A Sweepline Algorithm for Voronoi Diagrams, Proc. 2nd Ann. Symp. on Computational Geometry, ACM, 313–322, 1986.Google Scholar
  2. [SH 75]
    M. Shamos, D. Hoey: Closest-Point Problems, 16th Annual IEEE Symposium on Foundations of Computer Science, 151–162 (1975).Google Scholar
  3. [SH 76]
    M. Shamos, D. Hoey: Geometric intersection problems, 17th Annual IEEE Symposium on Foundations of Computer Science, 208–215 (1976).Google Scholar
  4. [V 86]
    P. Vaidya: An Optimal Algorithm for the All-Nearest-Neighbors Problem, Proc. 27th IEEE Symp. Foundations of Computer Science, 117–122, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Klaus Hinrichs
    • 1
  • Jurg Nievergelt
    • 1
  • Peter Schorn
    • 1
  1. 1.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA

Personalised recommendations