An approximation algorithm for k-center problem on a convex polygon

This paper studies the constrained version of the k-center location problem. Given a convex polygonal region, every point in the region originates a service demand. Our objective is to place k facilities lying on the region’s boundary, such that every point in that region receives service from its closest facility and the maximum service distance is minimized. This problem is equivalent to covering the polygon by k circles with centers on its boundary which have the smallest possible radius. We present an 1.8841-approximation polynomial time algorithm for this problem.