The Batcher-banyan self-routing network: universality and simplification

It is shown that the Batcher-banyan network performs as a universal self-routing switch when inputs with unassigned destinations are present. This is demonstrated by first proving that banyan networks can realize permutations represented by bitonic sequences, and then noting that the sorted output of the Batcher network can be viewed as a bitonic sequence. Two methods are proposed for reducing the complexity of the Batcher-banyan network. In the first method, one stage of the banyan network is eliminated by assigning proper destination tags to the unassigned inputs. In the second, a self-routing switch based on the binary-radix sorting scheme is shown to be more economical for a small number of lines