Optimal algorithm for approximate nearest neighbor searching

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

246 Scopus citations

Abstract

Let S denote a set of n points in d-dimensional space, Rd, and let dist(p,q) denote the distance between two points in any Minkowski metric. For any real ε > 0 and q ∈ Rd, a point p ∈ S is a (1+ε)-approximate nearest neighbor of q if, for all p′ ∈ S, we have dist (p,q)/dist(p′,q)≤(1+ε). We show how to preprocess a set of n points in Rd in O(n log n) time and O(n) space, so that given a query point q ∈ Rd, and ε>0, a (1+ε)-approximate nearest neighbor of q can be computed in O(log n) time. Constant factors depend on d and ε. We show that given an integer k≥1, (1+ε)-approximations to the k-nearest neighbors of q can be computed in O(k log n) time.

Original languageEnglish
Title of host publicationProceedings of the Annual ACM SIAM Symposium on Discrete Algorithms
PublisherPubl by ACM
Pages573-582
Number of pages10
ISBN (Print)0898713293
StatePublished - 1994
Externally publishedYes
EventProceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms - Arlington, VA, USA
Duration: 23 Jan 199425 Jan 1994

Publication series

NameProceedings of the Annual ACM SIAM Symposium on Discrete Algorithms

Conference

ConferenceProceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms
CityArlington, VA, USA
Period23/01/9425/01/94

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