Fault-tolerant de Bruijn and shuffle-exchange networks

This paper addresses the problem of creating a fault-tolerant interconnection network for a parallel computer. Three topologies, namely, the base-2 de Bruijn graph, the base-m de Bruijn graph, and the shuffle-exchange, are studied. For each topology an N+k node fault-tolerant graph is defined. These fault-tolerant graphs have the property that given any set of k node faults, the remaining N nodes contain the desired topology as a subgraph. All of the constructions given are the best known in terms of the degree of the fault-tolerant graph. We also investigate the use of buses to reduce the degrees of the fault-tolerant graphs still further.