Bounds for Non-blocking Switch Networks
James Clerk · 1990
We show that non-blocking n x n Benes networks of 2 x 2 switches must have at least n( n - 1) - (n 2 /4) switches. The proof uses a result concerning the maximum number of edges an n-node graph can have without containing any triangles. With communications and computing in mind, much current effort is being directed to switching of optical signals. One common experimental device is a 2-inlet, 2-outlet (2 x 2) switch, which either switches two signals straight through (fig. l.(a)) or crosses them over (fig l.(b)). Networks of these switches can be built in integrated-optic form using waveguides made by Titanium diffusion on a substrate of Lithium Niobate (LiNb03 ) (2), (4).