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Consider a metric space $(P,dist)$ with $N$ points whose doubling dimensionis a constant. We present a simple, randomized, and recursive algorithm thatcomputes, in $O(N \log N)$ expected time, the closest-pair distance in $P$. Togenerate recursive calls, we use previous results of Har-Peled and Mendel, andAbam and Har-Peled for computing a sparse annulus that separates the points ina balanced way.

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