Determination of the Topology of a Directed Network

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

Bounding network spectra for network design

The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation between the eigenvalues of weighted and unweighted networks, here I show that for a wide class of networks the dynamical behavior is tightly bounded by few network parameters. This result provides rigorous conditions for the design of networks with predefined dynamical properties and for the structural control of physical processes in complex systems. The results are illustrated using synchronization phenomena as a model process.Comment: 17 pages, 4 figure