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On evil twin networks and the value of limited randomized routing

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2 Author(s)
B. D. Alleyne ; PMC-Sierra Inc., San Jose, CA, USA ; I. D. Scherson

A dynamic two-stage Delta network (N inputs and outputs) is introduced and analyzed for permutation routing. The notion of evil twins is introduced and a deterministic procedure is given to route any permutation in no more than 24√N network cycles. Two limited randomized routing schemes are then analyzed. The first called Single Randomization yields on average at most N!+1 (N!=O(logN/loglogN)1 and is the greatest integer such that (N!)!≤N) network cycles and the second called Multiple Randomization yields on average at most upper bound [log(logN+1)]+2+1/N network cycles for any input permutation. The probability of any permutation requiring at least c network cycles more than the above average bounds is then shown to be at most 1/(c+1) for Single Randomization and 1/Nr for Multiple Randomization, respectively. It is then shown how the dynamic two-stage network can be physically realized as a three-stage network. Both the evil twin and Multiple Randomization algorithms have been integrated into an off-the-shelf ASIC from PMC-Sierra, Inc. (PM-73488) which has been designed as a building block for such a three-stage implementation. These routing schemes are also adapted to run on a recirculating network. Recirculation is used to effect a reshuffling of data as in the dynamic network, but with a considerable reduction in network cost.

Published in:

IEEE Transactions on Parallel and Distributed Systems  (Volume:11 ,  Issue: 9 )