Related papers: Entropy based Nearest Neighbor Search in High Dime…
Similarity search methods are widely used as kernels in various machine learning applications. Nearest neighbor search (NNS) algorithms are often used to retrieve similar entries, given a query. While there exist efficient techniques for…
Nearest neighbor search is a basic computational tool used extensively in almost research domains of computer science specially when dealing with large amount of data. However, the use of nearest neighbor search is restricted for the…
Given a reference set $R$ of $n$ points and a query set $Q$ of $m$ points in a metric space, this paper studies an important problem of finding $k$-nearest neighbors of every point $q \in Q$ in the set $R$ in a near-linear time. In the…
In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently…
In large scale systems, approximate nearest neighbour search is a crucial algorithm to enable efficient data retrievals. Recently, deep learning-based hashing algorithms have been proposed as a promising paradigm to enable data dependent…
Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…
In this paper, we report progress on answering the open problem presented by Pagh~[14], who considered the nearest neighbor search without false negatives for the Hamming distance. We show new data structures for solving the $c$-approximate…
One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network.…
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…
We take a first step towards a rigorous asymptotic analysis of graph-based approaches for finding (approximate) nearest neighbors in high-dimensional spaces, by analyzing the complexity of (randomized) greedy walks on the approximate near…
Approximate Nearest neighbor search (ANNS) is fundamental and essential operation in applications from many domains, such as databases, machine learning, multimedia, and computer vision. Although many algorithms have been continuously…
In Euclidean Uniform Facility Location (UFL), the input is a set of clients in $\mathbb{R}^d$ and the goal is to place facilities to serve them, so as to minimize the total cost of opening facilities plus connecting the clients. We study…
In this note, we show that one can use average embeddings, introduced recently in [Naor'20, arXiv:1905.01280], to obtain efficient algorithms for approximate nearest neighbor search. In particular, a metric $X$ embeds into $\ell_2$ on…
We study the following range searching problem in high-dimensional Euclidean spaces: given a finite set $P\subset \mathbb{R}^d$, where each $p\in P$ is assigned a weight $w_p$, and radius $r>0$, we need to preprocess $P$ into a data…
Consider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest…
Locality-sensitive hashing (LSH) is an important tool for managing high-dimensional noisy or uncertain data, for example in connection with data cleaning (similarity join) and noise-robust search (similarity search). However, for a number…
We propose the first \emph{local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean $k$-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1…
Motivated by Johnson--Lindenstrauss dimension reduction, amplitude encoding, and the view of measurements as hash-like primitives, one might hope to compress an $n$-point approximate nearest neighbor (ANN) data structure into $O(\log n)$…
Let $T$ be a tree space (or tree network) represented by a weighted tree with $t$ vertices, and $S$ be a set of $n$ stochastic points in $T$, each of which has a fixed location with an independent existence probability. We investigate two…
Let $P$ be a set of $n$ colored points. We develop efficient data structures that store $P$ and can answer chromatic $k$-nearest neighbor ($k$-NN) queries. Such a query consists of a query point $q$ and a number $k$, and asks for the color…