Computational geometry: an introduction
Computational geometry: an introduction
A randomized algorithm for closest-point queries
SIAM Journal on Computing
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
An optimal algorithm for the on-line closest-pair problem
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Maintaining the minimal distance of a point set in polylogarithmic time
Discrete & Computational Geometry
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Randomized data structures for the dynamic closest-pair problem
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
New techniques for some dynamic closest-point and farthest-point problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Rectangular Point Location and the Dynamic Closest Pair Problem
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
An optimal algorithm for closest pair maintenance (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximate Similarity Search in Extremely High-Dimensional Data Sets
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
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Let S be a set of n points in RD . It is shown that a range tree can be used to find an L∞ -nearest neighbor in S of any query point, in O((logn)D−1 loglogn) time. This data structure has size O(n(logn)D−1) and an amortized update time of O((logn)D−1 loglogn). This result is used to solve the (1+ &egr;)-approximate L2-nearest neighbor problem within the same bounds. In this problem, for any query point p, a point ∈ is computed such that the euclidean distance between p and q is at most (1+&egr;) times the euclidean distance between p and its true nearest neighbor. This is the first dynamic data structure for this problem having close to linear size and polylogarithmic query and update times.New dynamic data structures are given that maintain a closest pair of S. For D ≥ 3, a structure of size O(n) is presented with amortized update time O((logn)D− loglogn). For D = 2 and any non-negative integer constant k, structures of size O(nlogn/(loglogn)k) (resp. O(n)) are presented having an amortized update time of O(lognloglogn) (resp. O((logn)2/(loglogn)k)). Previously, no deterministic linear size data structure having polylogarithmic update time was known for this problem.