On non-blocking switching networks

A switching network may be informally described as a collection of single-pole, single-throw switches arranged so as to connect a set of terminals called inputs to another set of terminals called outputs. It is non-blocking if, given any set of connections from some of the inputs to some of the outputs, and an idle input terminal x and idle output terminal y, then it is possible to connect x to y without disturbing any of the existing connections. Denote by σ(a, b) the minimal number of switches necessary to connect a inputs to b outputs using a non-blocking network. We are interested in studying the growth of σ(a, a) as a ∞. Results of C. Clos show that σ(a, a) ⩽ C ae2√log a·log 2. We show that σ(a, a) ⩽ 8a(log2a)2.