Distributed MST and Broadcast with Fewer Messages, and Faster Gossiping

We present a distributed minimum spanning tree algorithm with near-optimal round complexity of Õ(D + √ n) and message complexity Õ(min{n3/2,m}). This is the first algorithm with sublinear message complexity and near-optimal round complexity and it improves over the recent algorithms of Elkin [PODC’17] and Pandurangan et al. [STOC’17], which have the same round complexity but message complexity Õ(m). Our method also gives the first broadcast algorithm with o(n) time complexity – when that is possible at all, i.e., when D = o(n) – and o(m) messages. Moreover, our method leads to an Õ( √ nD)-round GOSSIP algorithm with bounded-size messages. This is the first such algorithm with a sublinear round complexity. 2012 ACM Subject Classification Theory of computation → Distributed algorithms

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