Engineering the Divide-and-Conquer Closest Pair Algorithm

We improve the famous divide-and-conquer algorithm by Bentley and Shamos for the planar closest-pair problem. For n points on the plane, our algorithm keeps the optimal O(n log n) time complexity and, using a circle-packing property, computes at most 7n/2 Euclidean distances, which improves Ge et al.’s bound of (3n log n)/2 Euclidean distances. We present experimental results of our comparative studies on four different versions of the divide-and-conquer closest pair algorithm and propose two effective heuristics.