Abstract
A hardware-oriented algorithm for generating permutations is presented that takes as a theoretic base an iterative decomposition of the symmetric groupS n into cosets. It generates permutations in a new order. Simple ranking and unranking algorithms are given. The construction of a permutation generator is proposed which contains a cellular permutation network as a main component. The application of the permutation generator for solving a class of combinatorial problems on parallel computers is suggested.
Similar content being viewed by others
References
S. G. Akl,A new algorithm for generating derangements, BIT 20 (1980), 2.
G. H. Chen, Maw-Sheng Chern,Parallel generation of permutations and combinations, BIT 26 (1986), 277–283.
M. Cosnard, A. G. Ferreira,Generating permutations on a VLSI suitable linear network, The Computer Journal 32, 6 (1989), 571–573.
M. C. Er,Efficient generation of stack permutations in lexicographical order, Journal of Information Processing 9, 1 (1985), 17–19.
M. Garey, D. S. Johnson,Computers and Intractability. A Guide to the Theory of NP-completeness, W. H. Freeman and Co., San Francisco (1979).
P. Gupta, G. P. Bhattacharjee,Parallel derangement generation algorithm, BIT 29 (1989), 14–22.
P. Gupta, G. P. Bhattacharjee,Parallel generation of permutations, The Computer Journal 26, 2 (1983), 97–105.
M. Hall, L. J. Paige,Complete mappings of finite groups, Pacific Journal of Math. (1955), 541–549.
M. Hall,The Theory of Groups, Macmillan, New York (1959).
W. H. Kautz, K. N. Levitt, A. Waksman,Cellular interconneection arrays, IEEE Transactions on Computers, 17, 5 (1968), 443–451.
A. Kapralski,New methods for generation permutations, combinations and other combinatorial objects in parallel, to appear.
W. Lipski,More on permutation generation methods, Computing 23 (1979), 57–365.
L. Mirsky,Transversal Theory, Academic Press, N. Y., 1971.
M. Mor, A. S. Fraenkel,Permutation generation on vector processors, The Computer Journal, 25, 4 (1982), 423–428.
A. Y. Oruç, A. M. Oruç,Programming cellular permutation networks through decomposition of symmetric groups, IEEE Transactions on Computers 36, 7 (1987), 802–809.
E. M. Reingold, J. Nievergelt, N. Deo,Combinatorial Algorithms. Theory and Practice, Prentice-Hall Inc., Englewood Cliffs, N.J., 1977.
R. Sedgewick,Permutation generation methods, Computing Survey 9, 2 (1977), 137–164.
I. Semba,Generation of stack sequences in lexicographical order, Journal of Information Processing 5, 1 (1982), 17–20.
S. Zaks,A new algorithm for generation of permutations, BIT 24 (1984), 196–204.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kokosiński, Z. On generation of permutations through decomposition of symmetric groups into cosets. BIT 30, 583–591 (1990). https://doi.org/10.1007/BF01933207
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01933207