Efficient Planar Two-Center Algorithms

Jongmin Choi; Hee-Kap Ahn

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arXiv · 2006.10365

Efficient Planar Two-Center Algorithms

Jongmin Choi·Hee-Kap Ahn

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Abstract

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 $O(n \log n)$-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 $O(n\log n)$-time algorithm for the case that the input points are in convex position. Both results improve the previous best $O(n\log n\log\log n)$ bound on the problems.

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Jongmin Choi, Hee-Kap Ahn. 2020-06-18. Efficient Planar Two-Center Algorithms. https://arxiv.org/abs/2006.10365

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