Issue No. 12 - December (1992 vol. 41)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.214674
<p>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.</p>
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. , pp. 1627-1630, December 1992, doi:10.1109/12.214674