Michael J. Dinneen. Algebraic Methods for Efficient Network Constructions. Master's Thesis, Dept. of Computer Science, University of Victoria, P.O. Box 3055, Victoria, B.C., Canada~~V8W~3P6, oct 1991.
The design of computer networks and parallel processor configurations is a topic of increasing importance. Network designs which efficiently support communications between nodes are crucial for many applications. Cost and physical limitations generally prevent the nodes in a network from having more than a fixed number of hardware connections to other nodes (that is, the nodes must have bounded degree). This fundamental constraint makes the design problem nontrivial. The topic of this thesis is an explanation of ways in which group theory can be used to design bounded-degree communication-efficient networks. Our methods have yielded a number of network designs that are the largest known for networks satisfying specified bounds on node degree and either diameter or broadcast time, for values of these parameters that are in the range of potential engineering significance.