This paper considers the planar Euclidean two-center problem: given a planar n-point set S, nd two congruent circular disks of the smallest radius covering S. The main result is a deter-ministic algorithm with running time O(n log 2 n log 2 log n), improving the previous O(n log 9 n) bound of Sharir and almost matching the randomized O(n log 2 n) bound of Eppstein. If a point in the intersectio...