  We give a maximal independent set (MIS) algorithm that runs in $O(\log \log
\Delta)$ rounds in the congested clique model, where $\Delta$ is the maximum
degree of the input graph. This improves upon the $O(\frac{\log(\Delta) \cdot
\log \log \Delta}{\sqrt{\log n}} + \log \log \Delta )$ rounds algorithm of
[Ghaffari, PODC '17], where $n$ is the number of vertices of the input graph.
  In the first stage of our algorithm, we simulate the first
$O(\frac{n}{\text{poly} \log n})$ iterations of the sequential random order
Greedy algorithm for MIS in the congested clique model in $O(\log \log \Delta)$
rounds. This thins out the input graph relatively quickly: After this stage,
the maximum degree of the residual graph is poly-logarithmic. In the second
stage, we run the MIS algorithm of [Ghaffari, PODC '17] on the residual graph,
which completes in $O(\log \log \Delta)$ rounds on graphs of poly-logarithmic
degree.
