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COMPGEOM
2006
ACM

Lower bounds on locality sensitive hashing

9 years 4 months ago
Lower bounds on locality sensitive hashing
Given a metric space (X, dX), c ≥ 1, r > 0, and p, q ∈ [0, 1], a distribution over mappings H : X → N is called a (r, cr, p, q)-sensitive hash family if any two points in X at distance at most r are mapped by H to the same value with probability at least p, and any two points at distance greater than cr are mapped by H to the same value with probability at most q. This notion was introduced by Indyk and Motwani in 1998 as the basis for an efficient approximate nearest neighbor search algorithm, and has since been used extensively for this purpose. The performance of these algorithms is governed by the parameter ρ = log(1/p) log(1/q) , and constructing hash families with small ρ automatically yields improved nearest neighbor algorithms. Here we show that for X = 1 it is impossible to achieve ρ ≤ 1 2c . This almost matches the construction of Indyk and Motwani which achieves ρ ≤ 1 c .
Rajeev Motwani, Assaf Naor, Rina Panigrahy
Added 13 Jun 2010
Updated 13 Jun 2010
Type Conference
Year 2006
Where COMPGEOM
Authors Rajeev Motwani, Assaf Naor, Rina Panigrahy
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