Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn ¹c2/+o(1)) and space O(dn + n¹⁺¹c2/+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in (R. Motwani et al., 2006). 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/c2). Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech lattice