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Discrete & Computational Geometry

, Volume 20, Issue 3, pp 359–373 | Cite as

Approximate Nearest Neighbor Queries Revisited

  • T. M. Chan

Abstract.

This paper proposes new methods to answer approximate nearest neighbor queries on a set of n points in d -dimensional Euclidean space. For any fixed constant d , a data structure with O(\(\varepsilon\) (1-d)/2 n log n) preprocessing time and O(\(\varepsilon\) (1-d)/2 log n) query time achieves an approximation factor 1+\(\varepsilon\) for any given 0 < \(\varepsilon\) < 1; a variant reduces the \(\varepsilon\) -dependence by a factor of \(\varepsilon\) -1/2 . For any arbitrary d , a data structure with O(d 2 n log n) preprocessing time and O(d 2 log n) query time achieves an approximation factor O(d 3/2 ) . Applications to various proximity problems are discussed.

Keywords

Data Structure Euclidean Space Query Time Approximation Factor Dimensional Euclidean Space 
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.

Copyright information

© Springer-Verlag New York Inc. 1998

Authors and Affiliations

  • T. M. Chan
    • 1
  1. 1.Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124-4250, USA tchan@cs.miami.eduUS

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