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)
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Hausdorff distance under translation for points and balls
Proceedings of the nineteenth annual symposium on Computational geometry
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-time tradeoffs for approximate spherical range counting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the importance of idempotence
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The effect of corners on the complexity of approximate range searching
Proceedings of the twenty-second annual symposium on Computational geometry
Deformable spanners and applications
Computational Geometry: Theory and Applications
Journal of Computer and System Sciences
Nearest-neighbor-preserving embeddings
ACM Transactions on Algorithms (TALG)
Space-Time Tradeoffs for Proximity Searching in Doubling Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Space-time tradeoffs for approximate nearest neighbor searching
Journal of the ACM (JACM)
Deformable spanners and applications
Computational Geometry: Theory and Applications
Hausdorff distance under translation for points and balls
ACM Transactions on Algorithms (TALG)
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate nearest neighbor search for low dimensional queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Given a set S of n points in IRd, a (t, ε)-approximate Voronoi diagram (AVD) is a partition of space into constant complexity cells, where each cell c is associated with t representative points of S, such that for any point in c, one of the associated representatives approximates the nearest neighbor to within a factor of (1 + ε). The goal is to minimize the number and complexity of the cells in the AVD. We show that it is possible to construct an AVD consisting of O(n/εd) cells for t = 1, and O(n) cells for t = O(1/ε(d-1)/2). In general, for a real parameter 2 ≤ γ ≤ 1/ε, we show that it is possible to construct a (t, ε)-AVD consisting of O(nγd) cells for t = O(1/(εγ)(d-1)/2). The cells in these AVDs are cubes or differences of two cubes. All these structures can be used to efficiently answer approximate nearest neighbor queries. Our algorithms are based on the well-separated pair decomposition and are very simple.