Abstract
The concept of permutation-exchange graph is introduced to generalize the well known shuffle-exchange graph. A complete characterization of the permutations that give rise to emulators of the cube is also found, and it is shown that all these permutations are closely related to the shuffle.
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References
Stone, H. S., Parallel processing with the perfect shuffle.IEEE Trans. Comput. C-20, 2, (Feb. 1971) 153–161.
Pease, M. C., The indirect binaryn-cube microprocessor array.IEEE Trans. Comput. C-26, 5, (May 1977) 458–473.
Preparata, F. P., and Vuillemin, J., The cube-connected-cycles: A versatile network for parallel computation.CACM, 24, 5 (May 1981) 300–309.
Kleitman, D., Leighton, F. T., Lepley, M., and Miller, G. L., New layouts for the shuffle-exchange graph.Proc. 13th ACM Symp. on Th. of Computing, Milwaukee, Wisc., (May 1981); pp. 278–292.
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Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801.
This work was supported in part by an IBM Predoctoral Fellowship and in part by the National Science Foundation under Grant MCS-81-05552.
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Bilardi, G., Jin, X. Permutation-exchange graphs that emulate the binary cube. Math. Systems Theory 17, 193–198 (1984). https://doi.org/10.1007/BF01744440
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DOI: https://doi.org/10.1007/BF01744440