Construction for Group-Balanced Connecting Networks

An s -stage (connecting) network satisfies the following conditions: (i) The network is composed of switches and links. Switches are arranged in a sequence of s stages. (ii) The switches in a given stage are identical. In particular, they have the same size, i.e., the same number of input terminals and output terminals. (iii) Links can exist only between two switches in adjacent stages. In this paper, we assume that each switch is a rectangular (matrix) switch; i.e., there is a crosspoint connecting every input terminal with every output terminal of that switch. Figure 1 illustrates a three-stage network. Consider an s-stage network and let denote a switch in the ith stage. Consider the paths in the network which connect an Si (input switch), say, the kth, with an Ss (output switch), say the ;th. Taking the union of all such paths and replacing each switch on a path by a node, we have 1643 Fig. 1--Three-stage network.