Rearrangeable f-cast multi-log2 N networks

Multi-log₂ N networks (or vertically stacked banyan networks) have been an attractive class of switching networks due to their small depth O(log N), absolute signal loss uniformity and good fault tolerance property. Recently, F.K.Hwang extended the study of multi-log₂ N networks to the general f-cast case, which covers the unicast case (f = 1) and multicast case (f = N) as special cases, and determined the conditions for these networks to be f-cast strictly nonblocking when the fan-out capability is available at both the input stage and middle banyan stage. In this paper, we study the rearrangeable f-cast multilog₂ N networks under both node-blocking scenario (relevant to photonic switches) and link-blocking scenario (relevant to electronic switches). In particular, we consider the following three fan-out cases in our study: (1) no restriction on fan-out capability; (2) input stage has no fan-out capability; (3) middle banyan stage has no fan-out capability. We determine the necessary conditions for the first two cases while obtaining the necessary and also sufficient condition for the third one.