Brief Announcement: Towards a Complexity Theory for the Congested Clique.

The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of lower bounds for the congested clique; indeed, it is now know that proving explicit congested clique lower bounds is as difficult as proving circuit lower bounds. In this work, we use traditional complexity-theoretic tools to build a clearer picture of the complexity landscape of the congested clique, proving non-constructive lower bounds and studying the relationships between natural problems.