Functional and topological relations among banyan multistage networks of differing switch sizes

Relations among banyan multistage interconnection networks (MINs) of differing switch sizes are studied. If two N×N networks W and W´ have switch sizes r and s, respectively, and if r>s, then W realizes a larger number of permutations than W´. Consequently, the two networks can never be equivalent. However, W may realize all the permutations of W´, 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