  Given a set of point sites in a simple polygon, the geodesic farthest-point
Voronoi diagram partitions the polygon into cells, at most one cell per site,
such that every point in a cell has the same farthest site with respect to the
geodesic metric. We present an $O(n\log\log n+m\log m)$- time algorithm to
compute the geodesic farthest-point Voronoi diagram of $m$ point sites in a
simple $n$-gon. This improves the previously best known algorithm by Aronov et
al. [Discrete Comput. Geom. 9(3):217-255, 1993]. In the case that all point
sites are on the boundary of the simple polygon, we can compute the geodesic
farthest-point Voronoi diagram in $O((n + m) \log \log n)$ time.
