The PM22I Interconnection Network

For the interconnection networks of multiprocessors, performance measures such as the request acceptance probability and the network delay are known to improve as the hasic switch size increases. However, the network cost also increases at the same time. Thus, the choice of the switch size provides important cost versus performance tradeoffs once a particular network configuration has been decided upon. For the cube type networks, (2 x 2), (4 x 4), and (8 X 8) switches have been popular. However, for a class of interconnection networks based on the plus-minus-2‘ (PM2I) functions, such as the augmented data manipulator (ADM), the inverse augmented data manipulator (IADM), and the gamma network, a (3 x 3) switch has been the basic building block. In this paper, we show a scheme based on the standard multiplier recoding technique, which enables us to use (5 x 5) switches for the PMZI networks. The connections between switching stages are based on the modified PM2I functions, and are called plus-minus-2” (PM221). We call these new networks the PM22I networks. Manuscript received May 21, 1986; revised February 22, 1988. This work The authors are with the Department of Computer and Information Science, IEEE Log Number 8820895. was supported in part by The Ohio State University Seed Grant 221630. The Ohio State University, Columbus, OH 43210. Since the number of switching stages in the PM22I networks is one half of those in the PM2I networks, with a moderate increase in the switch size from (3 x 3) to (5 X 5), these networks provide similar design tradeoffs available by the (2 x 2) and (4 x 4) cube networks. Index Tenns-Interconnection network, multiplier recoding, performance analysis, plus-minus 2’ network, plus-minus 22i network, routing algorithm, tag recoding.