Self-routing in 2-D shuffle networks with dimension-dependent switches and interconnections

In shuffle multistage interconnection networks (MINs), by increasing the size of the switches, the number of stages (NS) and in turn the attenuation of signals decreases. An interesting concept for self-routing in shuffle MINs are dimension-dependent switches, i.e. switches of size 2^d×2^d (where d≥1 is the dimension of the interconnected data set) and dimension-dependent interconnections. Throughout the paper the 1-D shuffle interconnections and k×k-switches (k≥4) are replaced by d-dimensional shuffles (d≥2) and switches of size 2^d×2^d though the networks are still planar. In this way, given a data set, the original contribution of the paper is the presentation of (1) the number of topologically equivalent shuffle networks, (2) the complete concept of self-routing in (artificial) higher-dimensional shuffle networks (3) the solution of self-routing in 2-D shuffle networks not solvable by the common concept and (4) the decomposition of the input/output array into several small arrays without loss of functionality. The latter is important as presently reliable laser arrays have size of at most 8×8 and 16×16, respectively.