  The weighted $k$-center problem in graphs is a classical facility location
problem where we place $k$ centers on the graph, which minimize the maximum
weighted distance of a vertex to its nearest center. We study this problem when
the underlying graph is a cactus with $n$ vertices and present an $O(n \log^2
n)$ time algorithm for the same. This time complexity improves upon the
$O(n^2)$ time algorithm by Ben-Moshe et al. [TCS 2007], which is the current
state-of-the-art.
