 
Summary: Approximate Nearest Neighbor Queries in Fixed Dimensions
Sunil Arya
David M. Mount
Abstract
Given a set of n points in ddimensional Euclidean
space, S Ed
, and a query point q Ed
, we wish to
determine the nearest neighbor of q, that is, the point
of S whose Euclidean distance to q is minimum. The
goal is to preprocess the point set S, such that queries
can be answered as efficiently as possible. We assume
that the dimension d is a constant independent of n.
Although reasonably good solutions to this problem
exist when d is small, as d increases the performance
of these algorithms degrades rapidly. We present a
randomized algorithm for approximate nearest neighbor
searching. Given any set of n points S Ed
, and a
constant > 0, we produce a data structure, such that
