Near-optimal Hashing Algorithms For Approximate Nearest Neighbor In High Dimensions
Andoni A., Indyk. Arxiv 2024
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 logO(1) n space, with a query time of dnO(1/c2). Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech lattice
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