English

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 (P,dist)(P,dist) with NN points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in O(NlogN)O(N \log N) expected time, the closest-pair distance in PP. 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.

Keywords

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}
}
R2 v1 2026-06-23T14:49:12.981Z