Routing in the bidirectional shufflenet

We study the bidirectional shufflenet topology, which is obtained from the well-known (unidirectional) shufflenet by considering bidirectional links. More specifically, we define a shortest path routing algorithm, and derive the diameter and the average distance of the topology. The bidirectional shufflenet is then compared, in terms of average distance, with other variations of the perfect shuffle. Bidirectional links are very common in real networks. Possible applications of bidirectional shufflenets are wormhole routing electronic networks with back-pressure flow control, and wavelength routing optical networks. The former class of networks is considered, when virtual channels are used to prevent deadlocks. We show that four virtual channels are sufficient to avoid deadlocks in the bidirectional shufflenet, regardless of the number of nodes in the topology