Michael J. Dinneen, Nian Zhou. An Optimal Family of Bounded-Degree Broadcast Networks. Electronic Notes in Theoretical Computer Science, 78:196-208, 2003. [doi]
Increasingly, the design of efficient computer networks and multi-processor configurations are considered important applications of computer science. There are some constraints in network design which are usually created by economic and physical limitations. One constraint is the bounded degree, which is the limited number of connections between one node to others. Another possible constraint is a bound on the time that a message can afford to take during a ``broadcast''. We present, for the first time, a set of largest-known directed networks satisfied specified bounds on node degree and broadcast time. We also presents a family of optimal ($\Delta$, $\Delta+1$) broadcast digraphs. That is, digraphs with a proven maximum number of nodes, having maximum degree $\Delta$ and broadcast time at most $\Delta+1$.