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|a Andoni, Alexandr
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|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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|a Indyk, Piotr
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|a Razenshteyn, Ilya
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|a Nguyen, Huy L.
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|a Indyk, Piotr
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|a Razenshteyn, Ilya
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|a Beyond locality-sensitive hashing
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|b Association for Computing Machinery,
|c 2018-03-14T18:14:06Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/114155
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|a We present a new data structure for the c-approximate near neighbor problem (ANN) in the Euclidean space. For n points in R[superscript d], our algorithm achieves O[subscript c](n[superscript ρ] + d log n) query time and O[subscript c](n[superscript 1+ρ] + d log n) space, where ρ ≤ 7/(8c[superscript 2]) + O(1/c[superscript 3]) + o[subscript c](1). This is the first improvement over the result by Andoni and Indyk (FOCS 2006) and the first data structure that bypasses a locality-sensitive hashing lower bound proved by O'Donnell, Wu and Zhou (ICS 2011). By a standard reduction we obtain a data structure for the Hamming space and ℓ[subscript 1] norm with ρ ≤ 7/(8c)+ O(1/c[superscript 3/2])+ o[superscript c](1), which is the first improvement over the result of Indyk and Motwani (STOC 1998).
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|a en_US
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|a Article
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|t SODA '14 Proceedings of the Twenty-Fifth annual ACM-SIAM Symposium on Discrete Algorithms
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