We consider strongly-connected directed networks of identical synchronous, finite-state processors with in- and out-degree uniformly bounded by a network constant. Via a straightforward extension of Ostrovsky and Wilkerson's Backwards Communication Algorithm in [OW], we exhibit a protocol which solves the Global Topology Determination Problem, the problem of having the root processor map the global topology of a network of unknown size and topology, with running time O(ND) where N represents the number of processors and D represents the diameter of the network. A simple counting argument suffices to show that the Global Topology Determination Problem has time-complexity Omega(N logN) which makes the protocol presented asymptotically time-optimal for many large networks.

9 pages, no figures, accepted to appear in IPDPS 2002 (unable to attend), (journal version to appear in Information Processing Letters)