Self-Stabilizing Metric Graphs

We present a self-stabilizing algorithm for overlay networks that for an arbitrary given metric specified via a distance oracle constructs the graph representing that metric. The graph representing a metric is the unique minimal undirected graph such that for any pair of nodes the length of a shortest path between the nodes corresponds to the distance between the nodes according to the metric. The algorithm works under both an asynchronous and a synchronous dæmon. In the synchronous case, the algorithm stabilizes in time O ( n ), and after stabilization each node sends and receives only a constant number of messages per round.