Efficient K-Center Algorithms for Planar Points in Convex Position.

We present an efficient algorithm for the planar k -center problem for points in convex position under the Euclidean distance. Given n points in convex position in the plane, our algorithm computes k congruent disks of minimum radius such that each input point is contained in one of the disks. Our algorithm runs in O ( n 2 min { k , log n } log n + k 2 n log n ) time. This is the first polynomial-time algorithm for the k -center problem for points in convex position. For any fixed integer k , the running time is O ( n 2 log n ) . Our algorithm works with little modification for the k -center problem of points in convex position under the Minkowski distance of order p for any fixed positive integer p .