A sublinear time distributed algorithm for minimum-weight spanning trees

This paper considers the question of identifying the parameters governing the behavior of fundamental global network problems. Many papers on distributed network algorithms consider the task of optimizing the running time successful when an O(n) bound is achieved on an n-vertex network. We propose that a more sensitive parameter is the network's diameter Diam. This is demonstrated in the paper by providing a distributed minimum-weight spanning tree algorithm whose time complexity is sublinear in n, but linear in Diam (specifically, O(Diam + n^ϵ · log* n) for ϵ = (ln 3)/(ln 6) = 0.6131...). Our result is achieved through the application of graph decomposition and edge-elimination-by-pipelining techniques that may be of independent interest.