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Discrete & Computational Geometry

, Volume 4, Issue 2, pp 101–115 | Cite as

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

  • Pravin M. Vaidya
Article

Abstract

Given a setV ofn points ink-dimensional space, and anL q -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 metricL q . We give anO(n logn) algorithm for the all-nearest-neighbors problem, for fixed dimensionk and fixed metricL q . 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.

Keywords

Discrete Comput Geom Input Point Label Vertex Neighbor Problem Complete Binary Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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