On self-routing in Benes and shuffle-exchange networks

The authors present self-routing algorithms for realizing the class of linear permutations in various multistage networks such as Benes and 2n-stage shuffle-exchange. Linear permutations are useful in providing fast access of data arrays. In the first half of the network, switches are set by comparing the destination tags at their inputs, and, in the second half, switches are set using the Omega self-routing algorithm. It is shown that the comparison operations can be implemented in bit-serial networks without loss of time. In contrast, with the well-known Benes network self-routing algorithm of D. Nassimi and S. Sahni (1981), switches are set by giving priority to the destination tag at the upper input to them. The algorithms presented are useful in providing fast access of various data patterns using interconnection networks cheaper than crossbars