This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Optimal Fault-Tolerant Routing Algorithm for Double-Loop Networks
May 2001 (vol. 50 no. 5)
pp. 500-505

Abstract—A weighted double-loop network can be modeled by a directed graph $G(n;h_1,h_2;w_1,w_2)$ with vertex set $Z_n=\{0,1,\ldots,n-1\}$ and edge set $E=E_1\cup E_2$, where $E_1=\{(u,u+h_1)\;|\; u\in Z_n\}$, $E_2=\{(u,u+h_2)\;|\; u\in Z_n\}$. Assume that the weight of each edge in $E_1$ is $w_1$ and the weight of each edge in $E_2$ is $w_2$. In this paper, we present an optimal routing algorithm on double-loop networks under the case where there is at most one faulty element. Our algorithm is based on the fact that the shortest path from a vertex to any other vertex in a double-loop network is in the L-shape region.

[1] B.W. Arden and H. Lee, “Analysis of Chordal Ring Network,” IEEE Trans. Computers, vol. 30, pp. 291-295, 1981.
[2] Y. Cheng and F.K. Hwang, “Diameters on Weighted Double-Loop Networks,” J. Algorithms, vol. 9, pp. 401-410, 1988.
[3] Y. Cheng, F.K. Hwang, I.F. Akyildiz, and D.F. Hsu, “Routing Algorithms for Double-Loop Networks,” Int'l J. Foundations of Computer Science, vol. 3, no. 3, pp. 323-331, 1992.
[4] C.Y. Chou, D.J. Guan, and K.L. Wang, “A Dynamic Fault-Tolerant Message Routing Algorithm for Double-Loop Networks,” Information Processing Letters, vol. 70, pp. 259-264, 1999.
[5] D.Z. Du, D.F. Hsu, and F.K. Hwang, “Doubly Linked Ring Networks,” IEEE Trans. Computers, vol. 34, pp. 853-855, 1985.
[6] M. Escudero, J. Fiábrea, and P. Morillo, “Fault-Tolerant Routing in Double-Loop Networks,” Ars Combinatorial, vol. 25A, pp. 187-198, 1988.
[7] M.A. Fiol, “Applications of Graph Theory to Interconnection Networks,” PhD dissertation, Polytechnic Univ. of Barcelona, Spain, 1982.
[8] D.J. Guan, “An Optimal Message Routing Algorithm for Double-Loop Networks,” Information Processing Letters, vol. 65, pp. 255-260, 1998.
[9] F.K. Hwang, T.S. Lin, and R.H. Jan, “A Permutation Routing Algorithm for Double-Loop Networks,” Parallel Processing Letters, vol. 7, no. 3, pp. 259-265, 1997.
[10] D. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Reading, Mass., 1998.
[11] M.T. Liu, “Distributed Loop Computer Networks,” Advances in Computer, vol. 17, pp. 163-221, 1978.
[12] T.Y. Sung, C.Y. Lin, Y.C. Chuang, and L.H. Hsu, “Fault Tolerant Token Ring Embedding in Double-Loop Networks,” Information Processing Letters, vol. 66, pp. 201-207, 1998.

Index Terms:
Double-loop networks, fault-tolerant, optimal message routing.
Citation:
Yu-Liang Liu, Yue-Li Wang, D.J. Guan, "An Optimal Fault-Tolerant Routing Algorithm for Double-Loop Networks," IEEE Transactions on Computers, vol. 50, no. 5, pp. 500-505, May 2001, doi:10.1109/12.926162
Usage of this product signifies your acceptance of the Terms of Use.