Classification scheme for 3-D shuffle interconnection patterns

Two different types of the generalized perfect shuffle (GPS) and the generalized inverse shuffle (GIS) are considered in this paper: the standard symmetric GPS and GIS where a common basis exists for the numbering of both coordinates of the data array and the nonsymmetric GPS and GIS where each coordinate has a different basis. Additionally, the GPS is combined with the GIS providing the generalized mixed shuffle pattern. These shuffle patterns are transformed into their isomorphic 2-D counterparts and classified with respect to the number of standard perfect shuffle steps obtained by factorizing the permutations.