On self-routing in Clos connection networks

A self-routing connection network is a switching device where the routing of each switch can be determined in terms of the destination addresses of its inputs alone, i.e. independent of the routing information regarding the other switches in the network. One family of connection networks that were considered in the literature for self-routing are Clos networks. Earlier studies indicate that some Clos networks can be self-routed for certain permutations. In this paper, it is proved that the only category of Clos networks that can be self-routed for all permutations are those with at most two switches in their outer stages