The universality of a class of modified single-stage shuffle/exchange networks

A class of modified single-state shuffle/exchange (S/E) networks with reconfigurable connections is described. The capability of these modified networks to simulate every arbitrary permutation and other multistage S/E networks is studied. In particular, the upper bounds on simulating six multistage S/E networks are given. It is also shown that C.L. Wu and T.Y. Feng´s (1981) modified single-stage S/E network is optimal in terms of its universality and cost for the networks with one reconfigurable connection. However, some of the modified networks with two reconfigurable connections have better capability although they are slightly more expensive than Wu and Feng´s network. Also proposed is a link folding scheme that can be used to reduce the connection complexity of implementing the connection selection mechanism