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Efficient planar two-center algorithms
Computational Geometry ( IF 0.4 ) Pub Date : 2021-04-02 , DOI: 10.1016/j.comgeo.2021.101768
Jongmin Choi , Hee-Kap Ahn

We consider the planar Euclidean two-center problem in which given n points in the plane we are to find two congruent disks of the smallest radius covering the points. We present a deterministic O(nlogn)-time algorithm for the case that the centers of the two optimal disks are close to each other, that is, the overlap of the two optimal disks is a constant fraction of the disk area. We also present a deterministic O(nlogn)-time algorithm for the case that the input points are in convex position. Both results improve the previous best O(nlognloglogn) bound on the problems.



中文翻译:

高效的平面两中心算法

我们考虑平面欧几里德两中心问题,在该问题中,给定平面中的n个点,我们将找到两个半径最小的全等圆盘覆盖这些点。我们提出确定性Øñ日志ñ两个最佳磁盘的中心彼此靠近的情况下的实时算法,即两个最佳磁盘的重叠是磁盘区域的恒定分数。我们还提出了确定性Øñ日志ñ输入点处于凸位置的情况下的时间算法。两项结果均提高了以往的最佳水平Øñ日志ñ日志日志ñ 束手无策。

更新日期:2021-04-06
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