An analytical characterization of generalized shuffle-exchange networks

The shuffle-exchange network can be generalized by the definition of three parameters (n, r´, k). In a generalized shuffle-exchange (GSE) network, 2ⁿ inputs are first permuted by a shuffle such that an n-bit source address label is rotated left r´-bit positions to yield the destination address label. The exchange performs arbitrary permutations on 2^k ×2^k exchange switches. The GSE networks can emulate a variety of other networks, including orthogonally connected multidimensional cubes of all sizes, and they provide the possibility of incorporating alternate paths into networks without the addition of extra processing nodes or interconnections. Generalized shuffle-exchange networks are characterized herein by their connectivity, their diameter, and the number of alternate paths they permit