Abstract
This paper presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in Õ(D + √n) time and exchanges Õ(m) messages (both with high probability), where n is the number of nodes of the network, D is the diameter, and m is the number of edges. This is the first distributed MST algorithm that matches simultaneously the time lower bound of Ω(D + √n) [Elkin, SIAM J. Comput. 2006] and the message lower bound of Ω(m) [Kutten et al., J. ACM 2015], which both apply to randomized Monte Carlo algorithms.
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