A new decomposition algorithm for rearrangeable Clos interconnection networks

We give a new decomposition algorithm to route a rearrangeable three-stage Clos network in O(nr/sup 2/) time, which is faster than all existing decomposition algorithms. By performing a row-wise matrix decomposition, this algorithm routes all possible permutations, thus overcoming the limitation on realizable permutations exhibited by many other routing algorithms. This algorithm is extended to the fault tolerant Clos network which has extra switches in each stage, where it provides fault tolerance under faulty conditions and reduces routing time under submaximal fault conditions.