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Electronic Colloquium on Computational Complexity

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Reports tagged with nearest neighbor:
TR03-070 | 19th August 2003
Amit Chakrabarti, Oded Regev

An Optimal Randomised Cell Probe Lower Bound for Approximate Nearest Neighbour Searching

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 ... more >>>

TR05-117 | 17th September 2005
Piotr Indyk, David P. Woodruff

Polylogarithmic Private Approximations and Efficient Matching

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 >>>

TR19-055 | 9th April 2019
Kasper Green Larsen, Tal Malkin, Omri Weinstein, Kevin Yeo

Lower Bounds for Oblivious Near-Neighbor Search

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 >>>

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