Approximate Nearest Neighbor Queries Revisited (1998)
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@MISC{Chan98approximatenearest,
author = {Timothy M. Chan},
title = {Approximate Nearest Neighbor Queries Revisited},
year = {1998}
}
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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(" (1\Gammad)=2 n log n) preprocessing time and O(" (1\Gammad)=2 log n) query time achieves approximation factor 1 + " for any given 0 ! " ! 1; a variant reduces the "-dependence by a factor of " \Gamma1=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 approximation factor O(d 3=2 ). Applications to various proximity problems are discussed. 1 Introduction Let P be a set of n point sites in d-dimensional space IR d . In the well-known post office problem, we want to preprocess P into a data structure so that a site closest to a given query point q (called the nearest neighbor of q) can be found efficiently. Distances are measured under the Euclidean metric. The post office problem has many applications within computational...
