摘要
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.
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.
基金
This work is partially supported by Utah State University under Grant No.A13501.
