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We prove an $Omega(d lg n/ (lglg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $mathit{oblivious}$ approximate-near-neighbor search ($mathsf{ANN}$) 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 highest (non-oblivious) cell-probe lower bound for $mathsf{ANN}$. This is the first super-logarithmic $mathit{unconditional}$ lower bound for $mathsf{ANN}$ against general (non black-box) data structures. We also show that any oblivious $mathit{static}$ data structure for decomposable search problems (like $mathsf{ANN}$) can be obliviously dynamized with $O(log n)$ overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).
Graph search is one of the most successful algorithmic trends in near neighbor search. Several of the most popular and empirically successful algorithms are, at their core, a simple walk along a pruned near neighbor graph. Such algorithms consistentl
We present a new algorithm for the approximate near neighbor problem that combines classical ideas from group testing with locality-sensitive hashing (LSH). We reduce the near neighbor search problem to a group testing problem by designating neighbor
We prove that any two-pass graph streaming algorithm for the $s$-$t$ reachability problem in $n$-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits. As a corollary, we also obtain near-quadratic space lower bounds for several o
A recent series of papers by Andoni, Naor, Nikolov, Razenshteyn, and Waingarten (STOC 2018, FOCS 2018) has given approximate near neighbour search (NNS) data structures for a wide class of distance metrics, including all norms. In particular, these d
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a $(1+epsilon)$-approximati