Assigning Weights to Minimize the Covering Radius in the Plane

Given a set P of n points in the plane and a multiset W of k weights with k ≤ n, we assign each weight in W to a distinct point in P to minimize the maximum weighted distance from the weighted center of P to any point in P . In this paper, we give two algorithms which take O(kn log n) time and O(kn log k + kn log n) time, respectively. For a constant k, the second algorithm takes only O(n log n) time, which is near linear.