Topology of efficiently controllable banyan multistage networks

Due to their unique path property, banyan multistage interconnection networks (MINs) can be self-routed using control tags. The paper introduces a number of routing control classes of MINs and studies their structure. These include the D-controllable networks where the control tags are the destination labels, the FD-controllable networks, where the control tags are function of the destination labels and the doubly D- or FD-controllable networks which are D- or FD-controllable forward and backward. The paper shows that all D- and FD-controllable networks have a recursive structure, and that all doubly D-controllable (resp., FD-controllable) networks are strictly (resp., widely) functionally equivalent to the baseline network. The subclass of MINs where the interconnections are digit permute is also studied and shown to be doubly FD-controllable and hence equivalent to the baseline. Finally, the paper presents an efficient parallel algorithm that relabels the terminals of any one network to simulate any other network in that subclass