Optimal Boolean Locality-Sensitive Hashing
Abstract
For 0 ≤ β < α < 1 the distribution H over Boolean functions h \-1, 1\d \-1, 1\ that minimizes the expression equation* α, β = (1/h H \\ (x, y) α-corr.[h(x) = h(y)])(1/h H \\ (x, y) β-corr.[h(x) = h(y)]) equation* assigns nonzero probability only to members of the set of dictator functions h(x) = xi.
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