This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On Computing the Combinatorial Power of SW-Banyan Networks
May 1989 (vol. 38 no. 5)
pp. 761-765
The problem of calculating the combinatorial power of certain SW-banyan networks is related to a problem of enumerating certain matrices. Examples of two- and three-stage networks are used to demonstrate the technique. In each case, a polynomial-time algorithm is found to solve the problem. The results are presented for each case and certain asymptotic behavior is noted.

[1] G. B. Adams III and H. J. Siegel, "On the number of permutations performable by the augmented data manipulator network,"IEEE Trans. Comput., vol. C-31, pp. 270-227, Apr. 1982.
[2] R. A. Brualdi, "Matrices of zeros and ones with fixed row and column sum vectors,"Journal of Linear Algebra and Its Applications, North Holland, vol. 33, pp. 159-231, 1980.
[3] V. Cherkassky and M. Malek, "On permuting properties of regular rectangular SW-banyans,"IEEE Trans. Comput., vol. C-34, June 1985.
[4] D. DeGroot, "Expanding and contracting SW-banyan networks," inProc. Int. Conf. Parallel Processing, 1983, pp. 19-24.
[5] L. R. Goke and G. J. Lipovski, "Banyan networks for partitioning multiprocessor systems," inProc. 1st Annu. Symp. Comput. Architecture, Dec. 1973, pp. 21-28.
[6] I. P. Goulden and D. M. Jackson,Combinatorial Enumeration. New York: Wiley, 1984.
[7] S. C. Kothari, S. Lashmivarahan, and H. Peyravi, "Analysis of block-structured banyan networks," Tech. Rep., Univ. of Oklahoma School of Elec. Eng. Comput. Sci., Norman, OK, Jan. 1984.
[8] M. D. Palmer Leland, "On the power of the augmented data manipulator network," inProc. Int. Conf. Parallel Processing, 1985, pp. 74-78.
[9] R. S. Roberts and S. C. Kothari, "Computing the combinatorial power of SW-banyan networks," inProc. 18th Hawaii Int. Comput. Syst. Conf., Honolulu, HW, Jan. 1985, pp. 3-9.
[10] J. P. Shen, "Fault tolerance analysis of several interconnection networks," inProc. Int. Conf. Parallel Processing, 1982, pp. 102- 112.
[11] H. N. V. Temperley,Graph Theory and Applications. West Sussex, England: Ellis Hotwood, 1981.

Index Terms:
two-stage networks; combinatorial power; SW-banyan networks; matrices; three-stage networks; polynomial-time algorithm; asymptotic behavior; computational complexity; graph theory; matrix algebra.
Citation:
R.S. Roberts, S.C. Kothari, "On Computing the Combinatorial Power of SW-Banyan Networks," IEEE Transactions on Computers, vol. 38, no. 5, pp. 761-765, May 1989, doi:10.1109/12.24281
Usage of this product signifies your acceptance of the Terms of Use.