Assigning weights to minimize the covering radius in the plane

Abstract

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(k 2 n 2 log 3 n) time and O(k 5 n log 3 k + kn log 3 n) time, respectively. For a constant k, the second algorithm takes only O(n log 3 n) time, which is near linear.