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Fault-Tolerant Routing in Distributed Loop Networks
December 1995 (vol. 44 no. 12)
pp. 1452-1456

Abstract—The ring network is a popular network topology for implementation in local area networks and other configurations. But it has a disadvantage of high diameter and large communication delay. So loop networks were introduced with fixed-jump links added over the ring. In this paper, we characterize some values for the number of nodes for which the lower bound on the diameter of loop networks is achieved. We also give an O(δ) time algorithm (where δ is the diameter of the graph) for finding a shortest path between any two nodes of a general loop network. We also propose a scheme to find a near optimal path (not more than one over the optimal) in case of a single node or link failure.

[1] B.W. Arden and H. Lee,“Analysis of chordal ring,” IEEE Trans. Computers, vol. 30, pp. 291-292, 1981.
[2] P.J. Davis,Circulant Matrices.New York: John Wiley and Son, 1979.
[3] F.T. Boesch and R. Tindell,“Circulants and their connectivities,” J. Graph Theory, vol. 8, pp. 487-499, 1984.
[4] F.T. Boesch and J.-F. Wang,“Reliable circulant networks with minimum transmission delay,” IEEE Trans. Circuits and Systems, vol. 32, pp. 1,286-1,291, 1985.
[5] D.-Z. Du,D.-F. Hsu,Q. Li,, and J. Xu,“A combinatorial problem related to distributed loop networks,” Networks, vol. 20, pp. 173-180, 1990.
[6] C.K. Wong and D. Coppersmith, “A Combinatorial Problem Related to Multimodule Organizations,” J. ACM, vol. 21, pp. 392-402, July 1974.
[7] D. Tzvieli,“Minimal diameter double-loop networks. I. Large infinite optimal classes,” Networks, vol. 21, pp. 387-415, 1991.
[8] J.-C. Bermond and D. Tzvieli,“Minimal diameter double-loop networks. II. Dense optimal families,” Networks, vol. 21, no. 1, pp. 1-10, Jan. 1991.
[9] C.S. Raghavendra,M. Gerla,, and A. Avizienis,“Reliable loop topologies for large local computer networks,” IEEE Trans. Computers, vol. 34, no. 1, pp. 46-55, Jan. 1985.
[10] C.S. Raghavendra and J.A. Silvester,“A survey of multiconnected loop topologies for local computer networks,” Computer Networks and ISDN Systems, vol. 11, pp. 29-41, 1986.
[11] K. Mukhopadhyaya and B.P. Sinha,“Optimal design and routing of distributed loop networks,” Proc. IEEE Int’l Symp. Circuits and Systems, pp, 1,021-1,024, Aug.11-14, 1991.

Index Terms:
Diameter, link-fault, loop networks, network topology, node-fault, routing.
Krishnendu Mukhopadhyaya, Bhabani P. Sinha, "Fault-Tolerant Routing in Distributed Loop Networks," IEEE Transactions on Computers, vol. 44, no. 12, pp. 1452-1456, Dec. 1995, doi:10.1109/12.477250
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