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A celebrated technique for finding near neighbors for the angular distance involves using a set of \textit{random} hyperplanes to partition the space into hash regions [Charikar, STOC 2002]. Experiments later showed that using a set of…
Locality sensitive hashing (LSH) was introduced by Indyk and Motwani (STOC `98) to give the first sublinear time algorithm for the c-approximate nearest neighbor (ANN) problem using only polynomial space. At a high level, an LSH family…
We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this…
The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a general technique for constructing a data structure to answer approximate near neighbor queries by using a distribution $\mathcal{H}$ over locality-sensitive hash…
The $c$-approximate Near Neighbor problem in high dimensional spaces has been mainly addressed by Locality Sensitive Hashing (LSH), which offers polynomial dependence on the dimension, query time sublinear in the size of the dataset, and…
Nearest neighbor (NN) problem is an important scientific problem. The NN query, to find the closest one to a given query point among a set of points, is widely used in applications such as density estimation, pattern classification,…
To overcome the large memory requirement of classical lattice sieving algorithms for solving hard lattice problems, Bai-Laarhoven-Stehl\'{e} [ANTS 2016] studied tuple lattice sieving, where tuples instead of pairs of lattice vectors are…
Nearest-neighbor identification is central to the analysis of local structure in condensed matter systems. The solid-angle-based nearest-neighbor (SANN) algorithm is widely used offering a parameter-free and computationally efficient…
We study the fundamental problem of approximate nearest neighbor search in $d$-dimensional Hamming space $\{0,1\}^d$. We study the complexity of the problem in the famous cell-probe model, a classic model for data structures. We consider…
We investigate the problem of finding reverse nearest neighbors efficiently. Although provably good solutions exist for this problem in low or fixed dimensions, to this date the methods proposed in high dimensions are mostly heuristic. We…
We show an optimal data-dependent hashing scheme for the approximate near neighbor problem. For an $n$-point data set in a $d$-dimensional space our data structure achieves query time $O(d n^{\rho+o(1)})$ and space $O(n^{1+\rho+o(1)} +…
Given a large dataset of binary codes and a binary query point, we address how to efficiently find $K$ codes in the dataset that yield the largest cosine similarities to the query. The straightforward answer to this problem is to compare…
In this paper we study the problem of finding the approximate nearest neighbor of a query point in the high dimensional space, focusing on the Euclidean space. The earlier approaches use locality-preserving hash functions (that tend to map…
We show that approximate similarity (near neighbour) search can be solved in high dimensions with performance matching state of the art (data independent) Locality Sensitive Hashing, but with a guarantee of no false negatives. Specifically,…
There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes…
[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the $c$-Approximate Near Neighbor Search problem. For the $d$-dimensional Euclidean space and $n$-point datasets, we develop a data…
We study the problem of approximate near neighbor (ANN) search and show the following results: - An improved framework for solving the ANN problem using locality-sensitive hashing, reducing the number of evaluations of locality-sensitive…
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…
This work suggests faster and space-efficient index construction algorithms for LSH for Euclidean distance (\textit{a.k.a.}~\ELSH) and cosine similarity (\textit{a.k.a.}~\SRP). The index construction step of these LSHs relies on grouping…
Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since…