Determination of the Topology of a Directed Network
<|reference_start|>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.<|reference_end|>
@article{goldstein2003determination,
    title={Determination of the Topology of a Directed Network},
    author={Darin Goldstein},
    journal={arXiv preprint arXiv:cs/0310004},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0310004},
    primaryClass={cs.DC cs.DS}
}