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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^d, our algorithm achievesO(n^{\rho} + d log n) query time and O(n^{1 + \rho} + d log n) space, where\rho <= 7/(8c^2) + O(1 / c^3) + o(1). This is the first improvement over theresult by Andoni and Indyk (FOCS 2006) and the first data structure thatbypasses a locality-sensitive hashing lower bound proved by O'Donnell, Wu andZhou (ICS 2011). By a standard reduction we obtain a data structure for theHamming space and \ell_1 norm with \rho <= 7/(8c) + O(1/c^{3/2}) + o(1), whichis the first improvement over the result of Indyk and Motwani (STOC 1998).

Beyond Locality-Sensitive Hashing