A distributed algorithm for minimum weight spanning trees based on echo algorithms

A distributed algorithm based on echo algorithms is presented which constructs the minimum-weight spanning tree in a general undirected graph. In the worst case, the algorithm needs at most (2m+2(n-1) log (n/2)) messages and (2d log n) time, where d is the diameter of the network. In the best case, it needs only 2m messages and 2d time. The algorithm works in phases, and each phase consists of a down wave and an up wave. When the number of fragments is cut by at least one half in each phase, it needs at most O(log n) phases. On average, the algorithm needs only (m) messages and O(d) time. The algorithm itself is simple, so that other distributed algorithms based on it can be derived more easily.<>