A Simple Randomized $O(n \log n)$--Time Closest-Pair Algorithm in Doubling Metrics
Computational Geometry
2021-02-03 v1
Abstract
Consider a metric space with points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in expected time, the closest-pair distance in . To generate recursive calls, we use previous results of Har-Peled and Mendel, and Abam and Har-Peled for computing a sparse annulus that separates the points in a balanced way.
Cite
@article{arxiv.2004.05883,
title = {A Simple Randomized $O(n \log n)$--Time Closest-Pair Algorithm in Doubling Metrics},
author = {Anil Maheshwari and Wolfgang Mulzer and Michiel Smid},
journal= {arXiv preprint arXiv:2004.05883},
year = {2021}
}