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An optimal algorithm for approximate nearest neighbor searching fixed dimensions

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Arya, Sunil, Mount, David M., Netanyahu, Nathan S., Silverman, Ruth, Wu, Angela Y.·1998·Journal of the ACM
DOI 10.1145/293347.293348
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Abstract

Consider a set of 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 ∈ R d , is the closest point of S to q can be reported quickly. Given any positive real ϵ, data point p is a (1 +ϵ)- approximate nearest neighbor of q if its distance from q is within a factor of (1 + ϵ) 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 ∈ R d , and ϵ > 0, a (1 + ϵ)-approximate nearest neighbor of q can be computed in O ( c d , ϵ log n ) time, where c d,ϵ ≤ d ⌈1 + 6d/ϵ⌉ d is a factor depending only on dimension and ϵ. In general, we show that given an integer k ≥ 1, (1 + ϵ)-approximations to the k nearest neighbors of q can be computed in additional O(kd log n ) time.

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Metadata

Authors
Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., & Wu, A. Y.
Venue
Journal of the ACM
Publisher
Association for Computing Machinery (ACM)
Published
1998-11
Volume
45
Issue
6
Pages
891-923
ISSN
  • 0004-5411 (ISSN-L)
  • 1557-735X
DOI
10.1145/293347.293348
OpenAlex
W2427881153
Cited by
2,300
References
2
FWCI
37.55
Type
journal article
Language
en
Open access
bronze
Licence
www.acm.org/publications/policies/copyright_policy#Background (vor)

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Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., & Wu, A. Y. (1998). An optimal algorithm for approximate nearest neighbor searching fixed dimensions. Journal of the ACM. https://doi.org/10.1145/293347.293348

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