  The geodesic $k$-center problem in a simple polygon with $n$ vertices
consists in the following. Find a set $S$ of $k$ points in the polygon that
minimizes the maximum geodesic distance from any point of the polygon to its
closest point in $S$. In this paper, we focus on the case where $k=2$ and
present an exact algorithm that returns a geodesic $2$-center in $O(n^2\log^2
n)$ time.
