A distributed algorithm for finding all best swap edges of a minimum diameter spanning tree

Communication in networks suffers if a link fails. When the links are edges of a tree that has been chosen from an underlying graph of all possible links, a broken link even disconnects the network. Most often, the link is restored rapidly. A good policy to deal with this sort of transient link failures is swap rerouting, where the temporarily broken link is replaced by a single swap link from the underlying graph. A rapid replacement of a broken link by a swap link is only possible if all swap links have been precomputed. The selection of high quality swap links is essential; it must follow the same objective as the originally chosen communication subnetwork. We are interested in a minimum diameter tree in a graph with edge weights (so as to minimize the maximum travel time of messages). Hence, each swap link must minimize (among all possible swaps) the diameter of the tree that results from swapping. We propose a distributed algorithm that efficiently computes all of these swap links, and we explain how to route messages across swap edges with a compact routing scheme.