Related papers: A new near-linear time algorithm for k-nearest nei…
Reverse nearest neighbor queries are defined as follows: Given an input point-set P, and a query point q, find all the points p in P whose nearest point in P U {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor…
The Nearest Neighbor Search (NNS) problem asks to design a data structure that preprocesses an $n$-point dataset $X$ lying in a metric space $\mathcal{M}$, so that given a query point $q \in \mathcal{M}$, one can quickly return a point of…
Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…
Location-based services rely heavily on efficient methods that search for relevant points-of-interest (POIs) near a given location. A k Nearest Neighbor (kNN) query is one such example that finds the k closest POIs from an agent's location.…
We propose $\kappa$-approximate nearest neighbor (ANN) data structures for $n$ polygonal curves under the Fr\'{e}chet distance in $\mathbb{R}^d$, where $\kappa \in \{1+\varepsilon,3+\varepsilon\}$ and $d \geq 2$. We assume that every input…
Nearest neighbor (kNN) methods have been gaining popularity in recent years in light of advances in hardware and efficiency of algorithms. There is a plethora of methods to choose from today, each with their own advantages and…
A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…
In the \emph{$k$-Diameter-Optimally Augmenting Tree Problem} we are given a tree $T$ of $n$ vertices as input. The tree is embedded in an unknown \emph{metric} space and we have unlimited access to an oracle that, given two distinct…
Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor…
We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly…
Recently, there has been significant interest in the study of the community search problem in social and information networks: given one or more query nodes, find densely connected communities containing the query nodes. However, most…
Given an undirected graph $G$ with $m$ edges, $n$ vertices, and non-negative edge weights, and given an integer $k\geq 2$, we show that a $(2k-1)$-approximate distance oracle for $G$ of size $O(kn^{1 + 1/k})$ and with $O(\log k)$ query time…
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…
We define and investigate the problem of $\textit{c-approximate window search}$: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary…
We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Locality-sensitive hashing (LSH), introduced by Indyk and Motwani in STOC '98, has been an extremely influential framework for nearest neighbor search in high-dimensional data sets. While theoretical work has focused on the approximate…
The $k^2$-tree is a compact data structure designed to efficiently store sparse binary matrices by leveraging both sparsity and clustering of nonzero elements. This representation supports efficiently navigational operations and complex…
The Coxeter lattices, which we denote $A_{n/m}$, are a family of lattices containing many of the important lattices in low dimensions. This includes $A_n$, $E_7$, $E_8$ and their duals $A_n^*$, $E_7^*$ and $E_8^*$. We consider the problem…
We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest…