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Optimal lower bounds for locality sensitive hashing (except when q is tiny)
journal contribution
posted on 2005-02-01, 00:00 authored by Ryan O'Donnell, Yi Wu, Yuan ZhouWe 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.