Distributed MIS via All-to-All Communication

Computing a Maximal Independent Set (MIS) is a central problem in distributed graph algorithms. This paper presents an improved randomized distributed algorithm for congested clique model, defined as follows: Given a graph G=(V, E), initially each node knows only its neighbors. Communication happens in synchronous rounds over a complete graph, and per round each node can send O(log n) bits to each other node. We present a randomized algorithm that computes an MIS in Õ((log Δ)/(√(log n)) + 1 ) ≤ Õ(√(log Δ)) rounds of congested clique, with high probability. Here Δ denotes the maximum degree in the graph. This improves quadratically on the O(log Δ) algorithm of [Ghaffari, SODA'16]. The core technical novelty in this result is a certain local sparsification technique for MIS, which we believe to be of independent interest.