Throughout the paper, the proper operating of the self-routing principle in 2-D shuffle multistage interconnection networks (MINs) is analysed. (The notation 1-D MIN and 2-D MIN is applied for a MIN which interconnects 1-D and 2-D data, respectively.) Two different methods for self-routing in 2-D shuffle MINs are presented: (1) The application of self-routing in 1-D MINs by a switch-pattern preserving transformation of 1-D shuffle stages into 2-D shuffle stages (and vice versa) and (2) the general concept of self-routing in 2-D shuffle MINs based on self-routing with regard to each coordinate which is the original contribution of the paper. Several examples are provided which make the various problems transparent.

The polymer matrix for the number of N in-puts/outputs, N stages and 2x2-switches is denoted as the 1-D Spanke-Benes (SB) network. Throughout the paper, the 1-D SB-network, which equals the diamond cellular array, is extended to arbitrary dimensions by a mathematical transformation (a 1-D network provides the interconnection of 1-D data). This transformation determines the multistage architecture completely by providing size, location, geometry and wiring of the switches as well as it preserves properties of the networks, e.g., the capability of sorting. The SB-networks of dimension 3 are analysed and sorting is applied.

Throughout the paper, the nearest-neighbour (NN) interconnection of switches within a multistage interconnection network (MIN) is analysed. Three main results are obtained: (1) The switch preserving transformation of a 2-D MIN into the 1-D MIN (and vice versa) (2) The rearrangeability of the MIN and (3) The number of stages (NS) for the rearrangeable nonblocking interconnection. The analysis is extended to any dimension of the interconnected data set. The topological equivalence between 1-D MINs with NN interconnections (NN-MINs) and 1-D cellular arrays is shown.