Approximate Nearest Neighbor Search in $\ell_p$
نویسنده
چکیده
We present a new locality sensitive hashing (LSH) algorithm for c-approximate nearest neighbor search in lp with 1 < p < 2. For a database of n points in lp, we achieve O(dn ) query time and O(dn + n) space, where ρ ≤ O((ln c)/c). This improves upon the previous best upper bound ρ ≤ 1/c by Datar et al. (SOCG 2004), and is close to the lower bound ρ ≥ 1/c by O’Donnell, Wu and Zhou (ITCS 2011). The proof is a simple generalization of the LSH scheme for l2 by Andoni and Indyk (FOCS 2006).
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