An Optimized Divide-and-Conquer Algorithm for the Closest-Pair Problem in the Planar Case
Abstract
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.
Cite
@article{arxiv.1010.5908,
title = {An Optimized Divide-and-Conquer Algorithm for the Closest-Pair Problem in the Planar Case},
author = {José C. Pereira and Fernando G. Lobo},
journal= {arXiv preprint arXiv:1010.5908},
year = {2015}
}
Comments
This is a more complete version (14 pages) of the paper already published in the Journal of Computer Science and Technology (see Journal Reference)