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2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (2006)
Berkeley, California
Oct. 21, 2006 to Oct. 24, 2006
ISSN: 0272-5428
ISBN: 0-7695-2720-5
pp: 459-468
Alexandr Andoni , MIT, USA
Piotr Indyk , MIT, USA
ABSTRACT
We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O\left( {dn^{1/c^2 + o(1)} } \right) and space O\left( {dn + n^{1 + 1/c^2 + o(1)} } \right). This almost matches the lower bound for hashing-based algorithm recently obtained in [27]. We also obtain a space-efficient version of the algorithm, which uses dn+n log^{O(1)} n space, with a query time of dn^{O(1/c^2 )}. Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech Lattice.
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CITATION

P. Indyk and A. Andoni, "Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions," 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)(FOCS), Berkeley, California, 2006, pp. 459-468.
doi:10.1109/FOCS.2006.49
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