Abstract
This paper considers the planar Euclidean two-center problem: given a planar n-point set S, find two congruent circular disks of the smallest radius covering S. The main result is a deterministic algorithm with running time O( nlog 2 nlog 2log n), improving the previous O( nlog 9 n) bound of Sharir and almost matching the randomized O( nlog 2 n) bound of Eppstein. If a point in the intersection of the two disks is given, then we can solve the problem in O( nlog n) time with high probability.
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