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<p>Relations among banyan multistage interconnection networks (MINs) of differing switchsizes are studied. If two N*N networks W and W' have switch sizes r and s, respectively,and if r is greater than s, then W realizes a larger number of permutations than W'. Consequently, thetwo networks can never be equivalent. However, W may realize all the permutations ofW', in which case W is said to functionally cover W' in the strict sense. More generally, W is said to functionally cover W' in the wide sense if the terminals of W can be relabeled so that W realizes all the permutations of W'. Functional covering is topologically characterized, and an optimal algorithm to decide strict functional covering is developed.</p>
Index Termsfunctional relations; topological relations; banyan multistage networks; switch sizes;multistage interconnection networks; MINs; optimal algorithm; multiprocessorinterconnection networks
A. Youssef, B. Arden, "Functional and Topological Relations Among Banyan Multistage Networks of Differing Switch Sizes", IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 235-240, February 1993, doi:10.1109/71.207599
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