  Given a set $P$ of $n$ points in the plane and a multiset $W$ of $k$ weights
with $k\leq n$, 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 $O(k^2n^2\log^3
n)$ time and $O(k^5n\log^3k+kn\log^3 n)$ time, respectively. For a constant
$k$, the second algorithm takes only $O(n\log^3n)$ time, which is near linear.
