  This paper presents constant-time and near-constant-time distributed
algorithms for a variety of problems in the congested clique model. We show how
to compute a 3-ruling set in expected $O(\log \log \log n)$ rounds and using
this, we obtain a constant-approximation to metric facility location, also in
expected $O(\log \log \log n)$ rounds. In addition, assuming an input metric
space of constant doubling dimension, we obtain constant-round algorithms to
compute constant-factor approximations to the minimum spanning tree and the
metric facility location problems. These results significantly improve on the
running time of the fastest known algorithms for these problems in the
congested clique setting.
