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A Benes-Like Theorem for the Shuffle-Exchange Graph
December 1992 (vol. 41 no. 12)
pp. 1627-1630

One of the first theorems on permutation routing, proved by V.E. Benes (1965), shows that give a set of source-destination pairs in an N-node 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 constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in the Benes theorem.

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Index Terms:
shuffle-exchange graph; permutation routing; source-destination pairs; butterfly network; sources; destinations; total congestion; constant-congestion paths; off-line routing; necklaces; Benes theorem; computational complexity; graph theory; multiprocessor interconnection networks; parallel algorithms.
E.J. Schwabe, "A Benes-Like Theorem for the Shuffle-Exchange Graph," IEEE Transactions on Computers, vol. 41, no. 12, pp. 1627-1630, Dec. 1992, doi:10.1109/12.214674
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