Three-Stage Multiconnection Networks Which Are Nonblocking in the Wide Sense

A three-stage Clos network, denoted by v{m, ni, n, n2, /"·>), consists of r rectangular (/ii X m) input switches, m rectangular (ri X r2) middle switches and r> rectangular (m X n2) output switches. There is exactly one link connecting each input switch to each middle switch and one link connecting each middle switch to each output switch. The /i]/"i inlets of the input switches are called input terminals and the n>r> outlets of the output switches are called output terminals. Let I denote the set of input terminals and O the set of output terminals. A connecting pair in the classical sense is a pair (x,y)xE. I, y E O requesting to be connected. Masson and Jordan 1 generalized the definition of a connecting pair to be a pair (x, Y): x G /, Y C O such that jc is to be connected to every output terminal in Y. This definition was further generalized in Ref. 2 so that a connecting pair is a pair (X, Y): X C I, Y C O such that each terminal in X is to be connected to every terminal in Y. A network dealing with this type of connecting pairs is called a multiconnection network." In practice, we often need only consider X and Y with limited cardinalities. Let | S | denote the cardinality of a set S. Then in a (qi, q2) multiconnection 2183