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Optimal lower bounds for locality sensitive hashing (except when q is tiny)

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journal contribution
posted on 01.02.2005 by Ryan O'Donnell, Yi Wu, Yuan Zhou
We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest setting: point sets in {0; 1}d under the Hamming distance. Recall that H is said to be an (r; cr; p; q)-sensitive hash family if all pairs x; y ∈ {0; 1}d with dist(x; y) ≤ r have probability at least p of collision under a randomly chosen h ∈ H, whereas all pairs x; y ∈ {0; 1}d with dist(x; y) ≥ cr have probability at most q of collision. Typically, one considers d → ∞, with c > 1 fixed and q bounded away from 0.


Publisher Statement

Appears in Journal of Computer Security, vol. 13(1) (Roberto Gorrieri, editor), pp. 3-47, IOS Press, February 2005.