Asymmetrical multiconnection three-stage Clos networks

The authors study routing problems in a general class of asymmetrical three-stage Clos networks. This class covers many asymmetrical three-stage networks considered by earlier researchers. They derive necessary and sufficient conditions under which this class of networks is rearrangeable with respect to a set of multiconnections, that is, connections where the paired entities are not limited to single terminals but can be arbitrary subsets of the terminals. They model the routing problem in these networks as a network-flow problem. If the number of switching elements in the first and last stages of the network is O(f) and the number of switching elements in the middle stage is m, then the network-flow model yields a routing algorithm with running time O(mf³)