A simple randomized $O(n \log n)$–time closest-pair algorithm in doubling metrics

Authors

  • Michiel Smid
  • Anil Maheshwari
  • Wolfgang Mulzer

DOI:

https://doi.org/10.20382/jocg.v11i1a20

Abstract

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

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Published

2020-12-14

Issue

Vol. 11 No. 1 (2020)

Section

Articles

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