Kinetic Reverse $k$-Nearest Neighbor Problem

TL;DR

This paper introduces the first solution to the kinetic reverse $k$-nearest neighbor problem in fixed-dimensional Euclidean space, enabling dynamic querying of points for which a given query point is among their $k$-nearest neighbors.

Contribution

It presents the first algorithmic solution to the kinetic reverse $k$-nearest neighbor problem in $ eal^d$, handling moving points and dynamic queries.

Findings

First solution to kinetic reverse $k$-NN problem in $ eal^d$

Efficient handling of moving points and dynamic queries

Applicable in fixed-dimensional Euclidean spaces

Abstract

This paper provides the first solution to the kinetic reverse $k$-nearest neighbor (\rknn) problem in $\mathbb{R}^d$, which is defined as follows: Given a set $P$ of $n$ moving points in arbitrary but fixed dimension $d$, an integer $k$, and a query point $q\notin P$ at any time $t$, report all the points $p\in P$ for which $q$ is one of the $k$-nearest neighbors of $p$.