An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions

An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions (1994)

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by Sunil Arya , David M. Mount , Nathan S. Netanyahu , Ruth Silverman , Angela Y. Wu

Venue:	ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS
Citations:	634 - 29 self

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Datum	Value	Source
TITLE	An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions	user correction - Legacy Corrections
AUTHOR NAME	Sunil Arya	user correction
AUTHOR AFFIL	Department of Computer Science, The Hong Kong University of Science and Technology	user correction
AUTHOR ADDR	Clear Water Bay, Kowloon, Hong Kong	user correction
AUTHOR NAME	David M. Mount	user correction
AUTHOR AFFIL	Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland	user correction
AUTHOR ADDR	College Park, Maryland, 20742	user correction
AUTHOR NAME	Nathan S. Netanyahu	user correction
AUTHOR AFFIL	Dept. of Mathematics and Computer Science, Bar-Ilan University	user correction
AUTHOR ADDR	Ramat-Gan 52900, Israel.	user correction
AUTHOR NAME	Ruth Silverman	user correction
AUTHOR AFFIL	Department of Computer Science, University of the District of Columbia and University of the District of Columbia, Unuiversity of Maryland	user correction
AUTHOR ADDR	Washington, DC 20008	user correction
AUTHOR NAME	Angela Y. Wu	user correction
AUTHOR AFFIL	Department of Computer Science and Information Systems, The American University	user correction
AUTHOR ADDR	Washington, DC, 20016	user correction
ABSTRACT	Consider a set S of n data points in real d-dimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any positive real ffl, a data point p is a (1 + ffl)-approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a query point q 2 R d , and ffl ? 0, a (1 + ffl)-approximate nearest neighbor of q can be computed in O(c d;ffl log n) time, where c d;ffl d d1 + 6d=ffle d is a factor depending only on dimension and ffl. In general, we show that given an integer k 1, (1 + ffl)-approximations to the k nearest neighbors of q can be computed in additional O(kd log n) time.	user correction
YEAR	1994	user correction - Legacy Corrections
VENUE	ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS	user correction
VENUE TYPE	CONFERENCE	user correction
PAGES	573--582	user correction
CITATIONS	67 found	ParsCit 1.0