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E.J. Schwabe, "A BenesLike Theorem for the ShuffleExchange Graph," IEEE Transactions on Computers, vol. 41, no. 12, pp. 16271630, December, 1992.  
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@article{ 10.1109/12.214674, author = {E.J. Schwabe}, title = {A BenesLike Theorem for the ShuffleExchange Graph}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {12}, issn = {00189340}, year = {1992}, pages = {16271630}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.214674}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A BenesLike Theorem for the ShuffleExchange Graph IS  12 SN  00189340 SP1627 EP1630 EPD  16271630 A1  E.J. Schwabe, PY  1992 KW  shuffleexchange graph; permutation routing; sourcedestination pairs; butterfly network; sources; destinations; total congestion; constantcongestion paths; offline routing; necklaces; Benes theorem; computational complexity; graph theory; multiprocessor interconnection networks; parallel algorithms. VL  41 JA  IEEE Transactions on Computers ER   
One of the first theorems on permutation routing, proved by V.E. Benes (1965), shows that give a set of sourcedestination pairs in an Nnode butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constantcongestion paths for offline routing in the shuffleexchange graph is proved here. The necklaces of the shuffleexchange graph play the same structural role as the columns of the butterfly in the Benes theorem.
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