  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.
