The extra stage Gamma network

The augmented data manipulator (ADM), inverse augmented data manipulator (IADM), and the gamma network are based on the plus-minus-2 ⁱ connection patterns. In such a network, there exists multiple paths to connect a source S to a destination D except when S=D. The number of paths for ( S,D) is a function of the tag value (D-S ) modulo N, and the size of the network N. It is shown that by adding an extra stage to the PM2I interconnection network, multiple paths are provided for all the tag values including 0. The extra stage can be any stage out of n=log₂N stages of the original network. The analyses on the distribution of the number of paths for various tag values are performed for n possible choices of the extra stage. It is shown that the extra stage of 0, +1, -1 connection patterns gives the most uniform distribution, and also results in a 1-fault tolerant interconnection network