Related papers: A new near-linear time algorithm for k-nearest nei…
This paper is motivated by the k-nearest neighbors search: given an arbitrary metric space, and its finite subsets (a reference set R and a query set Q), design a fast algorithm to find all k-nearest neighbors in R for every point q in Q.…
This paper studies the important problem of finding all $k$-nearest neighbors to points of a query set $Q$ in another reference set $R$ within any metric space. Our previous work defined compressed cover trees and corrected the key…
The k-d tree is a classic binary space-partitioning tree used to organize points in k-dimensional space. While used in computational geometry and graphics, the data structure has a long history of application in nearest neighbor search. The…
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…
We introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of $n$ points $P=\{ x_1,\ldots, x_n\}$ in high-dimensions,…
The k-d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
Nearest-neighbor search dominates the asymptotic complexity of sampling-based motion planning algorithms and is often addressed with k-d tree data structures. While it is generally believed that the expected complexity of nearest-neighbor…
In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criterion. One is the distance criteria, and the other is the recall criteria.…
We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…
This paper proposes a new algorithm for reducing Approximate Nearest Neighbor problem to Approximate Near Neighbor problem. The advantage of this algorithm is that it achieves O(log n) query time. As a reduction problem, the uery time…
We present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain $P$ with $n$ vertices. Our goal is to store a dynamic set of $m$ point sites…
Let $k$ be a nonnegative integer. In the approximate $k$-flat nearest neighbor ($k$-ANN) problem, we are given a set $P \subset \mathbb{R}^d$ of $n$ points in $d$-dimensional space and a fixed approximation factor $c > 1$. Our goal is to…
In this paper we show that two-dimensional nearest neighbor queries can be answered in optimal $O(\log n)$ time while supporting insertions in $O(\log^{1+\varepsilon}n)$ time. No previous data structure was known that supports $O(\log…
The reverse $k$ nearest neighbor query finds all points that have the query point as one of their $k$ nearest neighbors, where the $k$NN query finds the $k$ closest points to its query point. Based on conics, we propose an efficent R$k$NN…
Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…