Beyond locality-sensitive hashing
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Beyond locality-sensitive hashing.pdf
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438.61 KB
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Author(s)
Andoni, Alexandr
Nguyen, Huy L.
Indyk, Piotr
Razenshteyn, Ilya
Date Issued
January 2014
Journal
SODA '14 Proceedings of the Twenty-Fifth annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Association for Computing Machinery
Citation
Andoni, Alexandr. "Beyond Locality-Sensitive Hashing." SODA '14 Proceedings of the Twenty-fifth Annual ACM-SIAM Aymposium on Discrete Algorithms, 5-7 January, 2014, Philadelphia, Pennsylvania, Association for Computing Machinery, 2014, pp. 1018-1028.
Version
Author's final manuscript
Abstract
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).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
http://dl.acm.org/citation.cfm?id=2634150&CFID=969998081&CFTOKEN=28708107
