  We study the problem of computing the Voronoi diagram of a set of $n^2$
points with $O(\log n)$-bit coordinates in the Euclidean plane in a
substantially sublinear in $n$ number of rounds in the congested clique model
with $n$ nodes. Recently, Jansson et al. have shown that if the points are
uniformly at random distributed in a unit square then their Voronoi diagram
within the square can be computed in $O(1)$ rounds with high probability
(w.h.p.). We show that if a very weak smoothness condition is satisfied by an
input set of $n^2$ points with $O(\log n)$-bit coordinates in the unit square
then the Voronoi diagram of the point set within the unit square can be
computed in $O(\log n)$ rounds in this model.
