Laying Out the Interconnection Network of the Transpose Bijection

Abstract

A subnetwork which performs the transpose bijection was used by Clos and others in the construction of interconnection networks. We consider the laying out of this subnetwork on the rectilinear grid.

It is assumed that the N = n ² inputs are arranged on one straight line, the N outputs on a parallel line and the connections are laid out in between. It is shown how this can be done in grid area 1/2 N ² + o(N ² ) , which is essentially optimal.

One of the consequences of this result is that the butterfly network with N = 2 ^2l input and output lines can also be laid out (optimally) in grid area 1/2 N ² + o(N ² ).