The Multimessage Unicast Capacity Region for Bidirectional Ring Networks

The capacity region for multiple unicast sessions on a bidirectional ring network is established and is shown to be achieved by routing. The result is proved in two parts. First, the routing (or multicommodity flow) region is characterized by two families of bounds. Second, rate upper bounds are derived that match those of the routing bounds. The upper bounds are based on extensions of progressive d-separating edge set bounds as well as tools from the literature on the multicommodity flow problem.