Publication 2000 Issue No. 9 - September Abstract - On Evil Twin Networks and the Value of Limited Randomized Routing
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On Evil Twin Networks and the Value of Limited Randomized Routing
September 2000 (vol. 11 no. 9)
pp. 910-925
 ASCII Text x Brian D. Alleyne, Isaac D. Scherson, "On Evil Twin Networks and the Value of Limited Randomized Routing," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 9, pp. 910-925, September, 2000.
 BibTex x @article{ 10.1109/71.879774,author = {Brian D. Alleyne and Isaac D. Scherson},title = {On Evil Twin Networks and the Value of Limited Randomized Routing},journal ={IEEE Transactions on Parallel and Distributed Systems},volume = {11},number = {9},issn = {1045-9219},year = {2000},pages = {910-925},doi = {http://doi.ieeecomputersociety.org/10.1109/71.879774},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Parallel and Distributed SystemsTI - On Evil Twin Networks and the Value of Limited Randomized RoutingIS - 9SN - 1045-9219SP910EP925EPD - 910-925A1 - Brian D. Alleyne, A1 - Isaac D. Scherson, PY - 2000KW - Multistage interconnection networks (MINs)KW - permutation routingKW - Clos networksKW - Delta networksKW - randomized routingKW - recirculating networksKW - SIMD computers.VL - 11JA - IEEE Transactions on Parallel and Distributed SystemsER -

Abstract—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 $2 \root 4 \of N$ network cycles. Two limited randomized routing schemes are then analyzed. The first called Single Randomization yields on average at most $N {\bar !}+1+{\frac{1}{N}}$ ($N {\bar !} =O({\frac{\log{N}}{\log\log{N}}})$1 and is the greatest integer such that $(N {\bar !} )! \leq N$) network cycles and the second called Multiple Randomization yields on average at most $\lfloor \log(\log{N}+1)\rfloor+2+{\frac{1}{N}}$ 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 ${\frac{1}{(c+1)!}}$ for Single Randomization and ${\frac{1}{N^{2^{c}}}}$ 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.

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Index Terms:
Multistage interconnection networks (MINs), permutation routing, Clos networks, Delta networks, randomized routing, recirculating networks, SIMD computers.
Citation:
Brian D. Alleyne, Isaac D. Scherson, "On Evil Twin Networks and the Value of Limited Randomized Routing," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 9, pp. 910-925, Sept. 2000, doi:10.1109/71.879774