An algorithm for approximate closest-point queries
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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)
Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Linear-size approximate voronoi diagrams
SODA '02 Proceedings of the thirteenth 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
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We present improved reductions of the nearest neighbor searching problem to Point Location in Balls by constructing linear size Approximate Voronoi Diagrams while maintaining the logarithmic search time. We do this first by simplifying the construction of Har-Peled[9] that reduces the number of balls generated by a logarithmic factor to O(n log n). We further reduce the number of balls by a new hierarchical decomposition scheme and a generalization of PLEBs to achieve linear space decomposition for nearest neighbor searching.