Discrete & Computational Geometry

, Volume 4, Issue 2, pp 101–115

AnO(n logn) algorithm for the all-nearest-neighbors Problem

  • Pravin M. Vaidya

DOI: 10.1007/BF02187718

Cite this article as:
Vaidya, P.M. Discrete Comput Geom (1989) 4: 101. doi:10.1007/BF02187718


Given a setV ofn points ink-dimensional space, and anLq-metric (Minkowski metric), the all-nearest-neighbors problem is defined as follows: for each pointp inV, find all those points inV−{p} that are closest top under the distance metricLq. We give anO(n logn) algorithm for the all-nearest-neighbors problem, for fixed dimensionk and fixed metricLq. Since there is an Θ(n logn) lower bound, in the algebraic decision-tree model of computation, on the time complexity of any algorithm that solves the all-nearest-neighbors problem (fork=1), the running time of our algorithm is optimal up to a constant factor.

Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Pravin M. Vaidya
    • 1
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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