平面最近邻问题的一种优化分治算法
An Optimized Divide-and-Conquer Algorithm for the Closest-Pair Problem in the Planar Case
摘要：
我们提出了一个工程版本的分而治之的算法，找到最接近的一对点，在一组给定的点在XY平面。对于这个版本的算法，我们表明，只有两个成对的比较，需要在结合步骤中，每个点，在于2三角洲宽的垂直板。算法的正确性示出了所有的Minkowski距离与p>=1。我们还表明，经验，虽然该算法的时间复杂度仍然是O（n lg n），减少比较的总数导致显着减少的总执行时间，输入的大小足够大。
英文摘要：
We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are required in the combine step, for each point that lies in the 2 delta-wide vertical slab. The correctness of the algorithm is shown for all Minkowski distances with p>=1. We also show empirically that, although the time complexity of the algorithm is still O(n lg n), the reduction in the total number of comparisons leads to a significant reduction in the total execution time, for inputs with size sufficiently large.
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