Wide-sense nonblocking for symmetric or asymmetric 3-stage Clos networks under various routing strategies

Beneš established the notion of wide-sense nonblocking by constructing an example on the symmetric 3-stage Clos network under packing which requires less hardware compared to strict nonblocking. This has remained the only example of a wide-sense non-blocking 3-stage Clos network which is not strictly nonblocking. In this paper, we study packing as well as several other routing strategies which have been studied in the literature and proved that no other example exists for the symmetric 3-stage Clos network. We then extend the study to asymmetric 3-stage Clos network for the first time. In particular, we extend Beneš example to asymmetric 3-stage Clos network and show that these are the only two possible examples for the strategies under study.