Amit Chakrabarti, Oded Regev

We consider the approximate nearest neighbour search problem on the

Hamming Cube $\b^d$. We show that a randomised cell probe algorithm that

uses polynomial storage and word size $d^{O(1)}$ requires a worst case

query time of $\Omega(\log\log d/\log\log\log d)$. The approximation

factor may be as loose as $2^{\log^{1-\eta}d}$ for any ...
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Piotr Indyk, David P. Woodruff

A private approximation of a function f is defined to be another function F that approximates f in the usual sense, but does not reveal any information about the input x other than what can be deduced from f(x). We give the first two-party private approximation of the Euclidean distance ... more >>>

Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search (ANN) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the ... more >>>