TY - GEN

T1 - Optimal algorithm for approximate nearest neighbor searching

AU - Arya, Sunil

AU - Mount, David M.

AU - Netanyahu, Nathan S.

AU - Silverman, Ruth

AU - Wu, Angela

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028257199&partnerID=8YFLogxK

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AN - SCOPUS:0028257199

SN - 0898713293

T3 - Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms

SP - 573

EP - 582

BT - Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms

PB - Publ by ACM

T2 - Proceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms

Y2 - 23 January 1994 through 25 January 1994

ER -