This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Optimally Routing LC Permutations on k-Extra-Stage Cube-Type Networks
January 1996 (vol. 45 no. 1)
pp. 97-103

Abstract—It is difficult to partition an arbitrary permutation into a minimum number of groups such that conflict-free paths for all source-destination pairs in each group can be established on an omega network. Based on linear algebra theory, this paper presents an optimal algorithm which solves this problem for the LC class of permutations on a large class of multi-stage networks. This algorithm extends the previous result which deals with the BPC class of permutations on the omega network.

[1] C. Wu and T. Feng,"The universality of the shuffle-exchange network," IEEE Trans. Computers, vol. 30, pp. 324-332, May 1981.
[2] D.P. Agrawal,"Graph theoretical analysis and design of multistage interconnection networks," IEEE Trans. Computers, vol. 32, pp. 637-648, July 1983.
[3] C. Wu and T. Feng,"On a class of multistage interconnection networks," IEEE Trans. Computers, vol. 29, pp. 694-702, Aug. 1980.
[4] G.B. Adams III and H.J. Siegel,"The extra stage cube: a fault-tolerant interconnection network for supersystems," IEEE Trans. Computers, vol. 31, pp. 443-454, May 1982.
[5] C.L. Wu,T.Y. Feng, and M.C. Lin,"Star: A local network system for real-time management of imagery data," IEEE Trans. Computers, vol. 31, pp. 923-933, Oct. 1982.
[6] I. Gazit and M. Malek,"On the number of permutations performable by extra-stage multistage interconnection networks," IEEE Trans. Computers, vol. 38, no. 2, pp. 297-302, Feb. 1989.
[7] C.T. Lea and D.J. Shyy,“Tradeoff of horizontal decomposition versus vertical stackingin rearrangeable nonblocking networks,” IEEE Trans. Communications, vol. 39, pp. 899-904, 1991.
[8] D.J. Shyy and C.T. Lea,“Log2(N,m,p) strictly nonblocking networks,” IEEE Trans. Communications, vol. 39, pp. 1,502-1,510, 1991.
[9] X. Shen,M. Xu, and X. Wang,"An optimal algorithm for permutation admissibility to multistage interconnection networks," IEEE Trans. Computers, vol. 44, no. 4, pp. 604-608, Apr. 1995.
[10] X. Shen,"An optimal O(NlgN) algorithm for permutation admissibility to extra-stage cube-type networks," IEEE Trans. Computers, vol. 44, no. 9, pp. 1,144-1,149, Sept. 1995.
[11] C.J.A. Hsia and C.Y. Chen,"Permutation capability of multistage interconnection networks," Proc. Int'l Conf. Parallel Processing, 1990, pp. I-338-346.
[12] C.S. Raghavendra and A. Varma,“Fault-tolerant multiprocessors with redundant-path interconnection networks,” IEEE Trans. Computers, vol. 35, No. 4, Apr. 1986.
[13] X. Shen,"Optimal realization of any BPC permutation on k-extra-etage cube-type networks," IEEE Trans. Computers, vol. 44, no. 5, pp. 714-719, May 1995.
[14] A. Sengupta,K. Zemoudeh, and S. Bandyopadhyay,"Self-Routing Algorithms for Strongly Regular Multistage Interconnection Networks," J. Parallel Distributed Computing vol. 14, pp. 187 - 192, 1992.
[15] C.S. Raghavendra and R.V. Boppana,"On self-routing in Benes and shuffle-exchange networks," IEEE Trans. Computers, vol. 40, no. 9, pp.1057-1064, Sept. 1991.
[16] K. Hwang and F.A. Briggs,Computer Architecture and Parallel Processing.New York: McGraw Hill, 1984.
[17] H.J. Siegel, Interconnection Networks for Large-Scale Parallel Processing, Second Ed., McGraw-Hill, New York, 1990.
[18] K. Hoffman and R. Kunze,linear algebra,Englewood Cliffs, NJ: Prentice Hall, 1971.
[19] D. Coppersmith and S. Winograd,"Matrix multiplication via arithmetic progressions," Proc. 19th Ann. Symp. Theory of Computing, pp. 1-6, 1987.

Index Terms:
k-extra-stage cube-type networks, LC permutations, multistage interconnection networks, optimization problems, permutation realization, routing.
Citation:
Qing Hu, Xiaojun Shen, Weifa Liang, "Optimally Routing LC Permutations on k-Extra-Stage Cube-Type Networks," IEEE Transactions on Computers, vol. 45, no. 1, pp. 97-103, Jan. 1996, doi:10.1109/12.481490
Usage of this product signifies your acceptance of the Terms of Use.