Optimal Algorithm for the Planar Two-Center Problem

07/17/2020

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by   Kyungjin Cho, et al.

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In this paper, we consider the planar two-center problem: Given a set S of n points in the plane, the goal is to find two smallest congruent disks whose union contains all points of S. We present an O(nlog n)-time algorithm for the planar two-center problem. This matches the best known lower bound of Ω(nlog n) as well as improving the previously best known algorithms which takes O(nlog^2 n) time.