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A Routing and Broadcasting Scheme on Faulty Star Graphs
November 1993 (vol. 42 no. 11)
pp. 1398-1403

The authors present a routing algorithm that uses the depth first search approach combined with a backtracking technique to route messages on the star graph in the presence of faulty links. The algorithm is distributed and requires no global knowledge of faults. The only knowledge required at a node is the state of its incident links. The routed message carries information about the followed path and the visited nodes. The algorithm routes messages along the optimal, i.e., the shortest path if no faults are encountered or if the faults are such that an optimal path still exists. In the absence of an optimal path, the algorithm always finds a path between two nodes within a bounded number of hops if the two nodes are connected. Otherwise, it returns the message to the originating node. The authors provide a performance analysis for the case where an optimal path does not exist. They prove that for a maximum of n-2 faults on a graph with N=n! nodes, at most 2i+2 steps are added to the path, where i is O( square root n). Finally, they use the routing algorithm to present an efficient broadcast algorithm on the star graph in the presence of faults.

[1] S.B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to then-cube," inProc. Int. Conf. Parallel Processing, 1987, pp. 393-400.
[2] S. B. Akers and B. Krishnamurthy, "A group theoretic model for symmetric interconnection networks," inProc. Int. Conf. Parallel Processing, 1986, pp. 216-223.
[3] S. B. Akers and B. Krishnamurthy, "The fault tolerance of star graphs," inProc. 2nd Int. Conf. Supercomput., 1987, pp. 270-276.
[4] M. A. Armstrong,Groups and Symmetry. New York: Springer-Verlag, 1988.
[5] D. M. Blough and N. Bagherzadeh, "Near-optimal message routing and broadcasting in faulty hypercubes,"Int. J. Parallel Programming, 1990.
[6] E. Horowitz and A. Zorat, "The binary trees as interconnection networks: Applications to multiprocessing systems and VLSI,"IEEE Trans. Comput., vol. C-30, pp. 247-253, 1981.
[7] S. Latifi and N. Bagherzadeh, "Incomplete star: An incrementally scalable network based on the star graph,"IEEE Trans. Parallel Distrib. Syst., to appear, Jan. 1994.
[8] D. K. Pradhan, "Dynamically restructurable fault-tolerant processor network architectures,"IEEE Trans. Comput., vol. C-34, pp. 434-447, 1985.
[9] S. Sur and P. K. Srimani, "A fault tolerant routing algorithm in star graph interconnection networks," inProc. Int. Conf. Parallel Processing, vol. 3, 1991, pp. 267-270.

Index Terms:
routing scheme; broadcasting scheme; faulty star graphs; depth first search; backtracking technique; faulty links; shortest path; optimal path; performance analysis; distributed algorithms; fault tolerant computing.
Citation:
N. Bagherzadeh, N. Nassif, S. Latifi, "A Routing and Broadcasting Scheme on Faulty Star Graphs," IEEE Transactions on Computers, vol. 42, no. 11, pp. 1398-1403, Nov. 1993, doi:10.1109/12.247843
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