Networks communicating for each pairing of terminals

Let G be a multigraph of maximum degree Ll and with a set oft vertices of degree one, called terminals. We call G a (Ll, t)-network if for any pairing of its terminals there exist edge-disjoint paths in G between those pairs (tis even). The concept of (Ll, t)-networks is introduced to model the situation when switching processors having Ll ports are to be connected in such a way that simultaneous communication is possible for any pairing of the free ports. We establish some properties of (Ll, f)-networks. In particular, we investigate optimal (or near-optimal) networks and obtain lower and upper bounds on the function n(Ll, t), the minimum number of interior nodes a (Ll, f)-network can have. © 1992 John Wiley & Sons, Inc.