On the Rearrangeability of Reverse Shuffle/Exchange Networks

This paper proposes a new rearrangeable algorithm in a multistage reverse shuffle/exchange network. Currently, the best upper bound for the rearrangeability of a shuffle/exchange network in nonsymmetric networks is 3logN-3 stages. We describe the rearrangeability of reverse shuffle/exchange multistage interconnection network on every arbitrary permutation with N\leqslant16. It can be established by setting two more stages in the middle stage of the network to allow the reduced network to be topological equivalent to a class of rearrangeable networks. The results enable us to establish an upper bound, 2logN+l stages for reverse shuffle/exchange network with N\leqslant16, and leads to the possibility of this bound when N\ge16.