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We consider the planar two-center problem for a convex polygon: given aconvex polygon in the plane, find two congruent disks of minimum radius whoseunion contains the polygon. We present an $O(n\log n)$-time algorithm for thetwo-center problem for a convex polygon, where $n$ is the number of vertices ofthe polygon. This improves upon the previous best algorithm for the problem.

Covering Convex Polygons by Two Congruent Disks