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 inÕ (D + √ n) time and exchangesÕ (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 rst distributed MST algorithm that matches simultaneously the time lower bound ofΩ(D + √ n) The prior time and message lower bounds are derived using two completely di erent graph constructions; the existing lower bound construction that shows one lower bound does not work for the other. To complement our algorithm, we present a new lower bound graph construction for which any distributed MST algorithm requires bothΩ(D + √ n) rounds and Ω(m) messages.
For example, in REF it is shown that there exists a randomized (Las Vegas) algorithm that runs in O( √ n + diameter(G)) rounds and uses O(m) messages (both w.h.p.).
A time- and message-optimal distributed algorithm for minimum spanning trees
STOC 2017
Computer Science