On rearrangeable networks with at most one reswitching

Abstract

It is well known that (applying usual notatios according to fig) tree stage connecting networks with m>r are non-blocking, if the method of rearrangement is applied, and that at most r-1 reswitchings are necessary. Pauli [4] stated that the number of reswitchings may be reduced by increasing the number m of middle switches. He showed that for networks with r=n and m=2n-2, the reswitching of one connection is always. In the present paper it is shown that for networks with m=2n-2, one reswitching is always sufficient .The results of this paper Figure 1. (m, n, r) switching network are proved by means of simple considerations and illustrated by examples.