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ACM Computing Surveys (CSUR)
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SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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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
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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
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Proceedings of the nineteenth annual symposium on Computational geometry
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A new digital watermarking scheme for 3D triangular mesh models
Signal Processing
Space-time tradeoffs for approximate nearest neighbor searching
Journal of the ACM (JACM)
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate polytope membership queries
Proceedings of the forty-third annual ACM symposium on Theory of computing
Data-driven trajectory smoothing
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Journal of Computer and System Sciences
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We present alternate reductions of the nearest neighbor searching problem to Point Location in Balls that reduces the space bound of Sariel Har-Peled's [S. Har-Peled, A replacement for Voronoi diagrams of near linear size, in: Proc. of IEEE FOCS, 2001, pp. 94-103, full version available from http://www.uiuc.edu/~sariel/papers] recent result on Approximate Voronoi Diagrams to linear while maintaining the logarithmic search time. We do this by simplifying the construction of [S. Har-Peled, A replacement for Voronoi diagrams of near linear size, in: Proc. of IEEE FOCS, 2001, pp. 94-103, full version available from http://www.uiuc. edu/~sariel/papers] that reduces the number of balls generated by algorithm 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. The construction of our data structures takes O(n log n) time.