Beyond locality-sensitive hashing
Author(s)Andoni, Alexandr; Nguyen, Huy L.; Indyk, Piotr; Razenshteyn, Ilya
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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).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
SODA '14 Proceedings of the Twenty-Fifth annual ACM-SIAM Symposium on Discrete Algorithms
Association for Computing Machinery
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.
Author's final manuscript