The Capacity Region of a Collection of Multicast Sessions in an Undirected Ring Network

A finite set of inequalities is given that characterizes the routing rate region for an undirected ring network in which the source and destination vertices of each communication session form a string of adjacent vertices. The result uses an extension of the Japanese theorem for communication problems with multiple multicast sessions and an interpretation of the extension in terms of the collection of minimum length routing trees for the various multicast sessions. It is further demonstrated that routing is rate optimal in this case using new extensions to progressive d-separating edge set bounds.