On the Number of Permutations Performable by the Augmented Data Manipulator Network

The Augmented Data Manipulator (ADM) network has been proposed as an interconnection network for SIMD machines. As one measure for comparing the ADM network to multistage cube networks, the number of distinct data permutations performable in a single pass through the ADM is examined. Techniques are given to count the number of settings of any stage of the network which are permutations. Upper and lower bounds on the number of distinct permutations performable by the network are proven.