Reverse nearest neighbor queries in fixed dimension

TL;DR

This paper introduces an efficient data structure for reverse nearest neighbor queries in fixed-dimensional Euclidean space, achieving optimal space, preprocessing, and query times.

Contribution

It presents a novel data structure that answers reverse nearest neighbor queries with linear space, near-linear preprocessing, and logarithmic query time.

Findings

Uses O(n) space for data storage

Preprocessing time is O(n log n)

Query time is O(log n)

Abstract

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 queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).