Papers › A Simple Randomized O(n logn)--Time Closest-Pair Algorithm in Doubling Metrics
A Simple Randomized O(n logn)--Time Closest-Pair Algorithm in Doubling Metrics
Anil Maheshwari, Wolfgang Mulzer, Michiel Smid
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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 logN) 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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