Related papers: Chromatic $k$-Nearest Neighbor Queries

In the $(1+\varepsilon,r)$-approximate near-neighbor problem for curves (ANNC) under some distance measure $\delta$, the goal is to construct a data structure for a given set $\mathcal{C}$ of curves that supports approximate near-neighbor…

In the Priority $k$-Supplier problem the input consists of a metric space $(F \cup C, d)$ over set of facilities $F$ and a set of clients $C$, an integer $k > 0$, and a non-negative radius $r_v$ for each client $v \in C$. The goal is to…

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for…

An instance of colorful k-center consists of points in a metric space that are colored red or blue, along with an integer k and a coverage requirement for each color. The goal is to find the smallest radius \r{ho} such that there exist…

This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects. In contrast with most existing approaches, we can only access the ``hidden'' space in which…

We study a geometric facility location problem under imprecision. Given $n$ unit intervals in the real line, each with one of $k$ colors, the goal is to place one point in each interval such that the resulting \emph{minimum color-spanning…

Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries and present a simple, fast, and highly practical data…

Let $V$ be a vector space of dimension $v$ over a field of order $q$. The $q$-Kneser graph has the $k$-dimensional subspaces of $V$ as its vertices, where two subspaces $\alpha$ and $\beta$ are adjacent if and only if $\alpha\cap\beta$ is…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…

The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…

Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…

Approximate near-neighbors search (\textsc{ANNS}) is a long-studied problem in computational geometry. %that has received considerable attention by researchers in the community. In this paper, we revisit the problem and propose the first…

Demands for minimum parameter setup in machine learning models are desirable to avoid time-consuming optimization processes. The $k$-Nearest Neighbors is one of the most effective and straightforward models employed in numerous problems.…

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…

Computing $k$-Nearest Neighbors (KNN) is one of the core kernels used in many machine learning, data mining and scientific computing applications. Although kd-tree based $O(\log n)$ algorithms have been proposed for computing KNN, due to…

Feature correspondence selection is pivotal to many feature-matching based tasks in computer vision. Searching for spatially k-nearest neighbors is a common strategy for extracting local information in many previous works. However, there is…

A $q$-\emph{equitable coloring} of a graph $G$ is a proper $q$-coloring such that the sizes of any two color classes differ by at most one. In contrast with ordinary coloring, a graph may have an equitable $q$-coloring but has no equitable…

Image search engines rely on appropriately designed ranking features that capture various aspects of the content semantics as well as the historic popularity. In this work, we consider the role of colour in this relevance matching process.…

[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…