A Simple Randomized O(n log n)–Time Closest-Pair Algorithm in Doubling Metrics

04/13/2020

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by   Anil Maheshwari, et al.

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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.