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We present a randomized algorithm that computes a Minimum Spanning Tree (MST) in O(log* n) rounds, with high probability, in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially each node knows only its incident edges, and per round each two nodes can exchange O(log n) bits. Our key technical novelty is an O(log* n) Graph Connectivity algorithm, the heart of which is a (recursive) forest growth method, based on a combination of two ideas: a sparsity-sensitive sketching aimed at sparse graphs and a random edge sampling aimed at dense graphs. Our result improves significantly over the O(log log log n) algorithm of Hegeman et al. [PODC 2015] and the O(log log n) algorithm of Lotker et al. [SPAA 2003; SICOMP 2005].

MST in Log-Star Rounds of Congested Clique