Optimal broadcasting in binary de Bruijn networks and hyper-deBruijn networks

The order-(m, n) hyper-deBruijn graph H D(m, n) is the direct product of an order-m hypercube and an order-n deBruijn graph. The hyper-deBruijn graph offers flexibility in terms of connections per node and the level of fault-tolerance. These networks as well possess logarithmic diameter, simple routing algorithms and support many computationally important subgraphs and admit efficient implementation. The authors present asymptotically optimal one-to-all (OTA) broadcasting scheme for these networks, assuming packet switched routing and concurrent communication on all ports. The product structure of the hyper-deBruijn graphs is exploited to construct an optimal number of edge-disjoint spanning trees to achieve this. Also, as an intermediate result they present a technique to construct an optimal number of spanning trees with heights bounded by the diameter in binary deBruijn graphs. This result is used to achieve the fastest OTA broadcasting scheme for binary deBruijn networks. The recent renewed interest of binary deBruijn networks makes this result valuable.<>