Distributed MST
Soumyottam Chatterjee, Gopal Pandurangan, Nguyen Dinh Pham · 2020
We study smoothed analysis of distributed graph algorithms, focusing on the fundamental minimum spanning tree (MST) problem. With the goal of studying the time complexity of distributed MST as a function of the "perturbation" of the input graph, we posit a smoothing model that is parameterized by a smoothing parameter 0 ≤ ϵ(n) ≤ 1 which controls the amount of random edges that can be added to an input graph G per round. Informally, ϵ(n) is the probability (typically a small function of n, e.g., n--¼) that a random edge can be added to a node per round. The added random edges, once they are added, can be used (only) for communication.