Construction for Group-Balanced Connecting Networks
F. K. Hwang, T. C. Liang · Bell System Technical Journal · 1977
We generalize the concept of balanced network to group-balanced network. An s-stage network is called a group-balanced network if its input switches can be partitioned into groups and its output switches into groups such that the connection pattern (called channel graph) between an input group and an output group is independent of which groups we choose. We show by construction that under a simple divisibility condition, a group-balanced network can be constructed satisfying the following requirements: (I) the number of stages is specified, (ii) the size of the switches in each stage is specified, (iii) the channel graph between an input group and an output group is specified.