This Article 
 Bibliographic References 
 Add to: 
Notes on Shuffle/Exchange Type Permutation Sets
July 1990 (vol. 39 no. 7)
pp. 962-965

Properties of some shuffle/exchange type permutation sets are studied from operational points of view. The permutation sets studied are Omega , Omega /sup -1/, Psi , L, and U; Omega and Omega /sup -1/ are, respectively, the omega and inverse omega permutation sets, Omega identical to ( Omega intersection Omega /sup -1/); and L and U are, respectively, the admissible lower and upper triangular permutation sets. Several intuitive operations are introduced. Based on these operations, important known results relating to these sets are readdressed. The recursive nature of the sets is also discussed.

[1] K. E. Batcher, "Sorting networks and their applications," inProc. AFIPS Conf., 1986, pp. 307-314.
[2] S.-T. Huang and S. K. Tripathi, "Finite state model and compatibility theory: New analysis tools for permutation networks,"IEEE Trans. Comput., vol. C-35, no. 7, pp. 591-601, July 1986.
[3] S.-T. Huang and S. K. Tripathi, "Self-routing technique in perfect-shuffle networks using control tags,"IEEE Trans. Comput., vol. 37, no. 2, pp. 251-256, Feb. 1988.
[4] D. H. Lawrie, "Access and alignment of data in an array processor,"IEEE Trans. Comput., vol. 24, no. 12, pp. 1145-1155, Dec. 1975.
[5] J. Lenfant, "Parallel permutations of data: A Benes network control algorithm for frequently used permutations,"IEEE Trans. Comput., vol. C-27, no. 7, pp. 637-647, July 1978.
[6] D. Nassimi and S. Sahni, "A self-routing Benes network and parallel permutation algorithms,"IEEE Trans. Comput., vol. C-30, no. 5, pp. 332-339, May 1981.
[7] D. S. Parker, "Notes on shuffle/exchange-type switching networks,"IEEE Trans. Comput., vol. C-29, no. 3, pp. 213-221, Mar. 1980.
[8] M. C. Pease, "The indirect binaryn-cube microprocessor array,"IEEE Trans. Comput., vol. C-26, no. 5, pp. 458-473, May 1977.
[9] D. Steinberg, "Invariant properties of the shuffle-exchange and a simplified cost-effective version of the Omega network,"IEEE Trans. Comput., vol. C-32, no. 5, pp. 444-450, May 1983.
[10] H. S. Stone, "Parallel processing with perfect shuffle,"IEEE Trans. Comput., vol. C-20, pp. 153-161, Feb. 1971.
[11] C. Wu and T.-Y. Feng, "On a class of multistage interconnection networks,"IEEE Trans. Comput., vol. C-29, no. 8, pp. 694-702, Aug. 1980.

Index Terms:
shuffle/exchange type permutation sets; intuitive operations; multiprocessor interconnection networks.
S.-T. Huang, "Notes on Shuffle/Exchange Type Permutation Sets," IEEE Transactions on Computers, vol. 39, no. 7, pp. 962-965, July 1990, doi:10.1109/12.55699
Usage of this product signifies your acceptance of the Terms of Use.