A randomized algorithm for closest-point queries
SIAM Journal on Computing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
Point location in arrangements of hyperplanes
Information and Computation
Randomized algorithms
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Photobook: content-based manipulation of image databases
International Journal of Computer Vision
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Exact L∞ nearest neighbor search in high dimensions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Closest-point problems simplified on the RAM
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
When Is ''Nearest Neighbor'' Meaningful?
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Contrast Plots and P-Sphere Trees: Space vs. Time in Nearest Neighbour Searches
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Fast Nearest Neighbor Search in Medical Image Databases
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Efficient Image Retrieval through Vantage Objects
VISUAL '99 Proceedings of the Third International Conference on Visual Information and Information Systems
Deflating the Dimensionality Curse Using Multiple Fractal Dimensions
ICDE '00 Proceedings of the 16th International Conference on Data Engineering
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Array-index: a plug&search K nearest neighbors method for high-dimensional data
Data & Knowledge Engineering
Approximate voronoi cell computation on spatial data streams
The VLDB Journal — The International Journal on Very Large Data Bases
VoR-tree: R-trees with Voronoi diagrams for efficient processing of spatial nearest neighbor queries
Proceedings of the VLDB Endowment
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We consider the problem of nearest-neighbor search for a set of n data points in d-dimensional Euclidean space. We propose a simple, practical data structure, which is basically a directed acyclic graph in which each node has at most two outgoing arcs. We analyze the performance of this data structure for the setting in which the n data points are chosen independently from a d-dimensional ball under the uniform distribution. In the average case, for fixed dimension d, we achieve a query time of O(log2 n) using only O(n) storage space. For variable dimension, both the query time and the storage space are multiplied with a dimension-dependent factor that is at most exponential in d. This is an improvement over previously known time-space tradeoffs, which all have a super-exponential factor of at least d驴 (d) either in the query time or in the storage space. Our data structure can be stored efficiently in secondary memory: In a standard secondary-memory model, for fixed dimension d, we achieve average-case bounds of O((log2 n)/B + log n) query time and O(N) storage space, where B is the block-size parameter and N = n/B. Our data structure is not limited to Euclidean space; its definition generalizes to all possible choices of query objects, data objects, and distance functions.