This Article 
 Bibliographic References 
 Add to: 
Fault-Tolerant Networks Based on the de Bruijn Graph
October 1991 (vol. 40 no. 10)
pp. 1167-1174

The authors introduce a novel class of networks based on the de Bruijn graph. These directed graphs are regular of degree, have N=k/sup n/ vertices for some n, and can tolerate up to k-2 node faults. Their fault-free diameter is n=log/sub k/N, and this is increases by at most 1 hop in the presence of k-2 faults. This class is very rich: for any given N=k/sup n/, one can construct at least 2/sup N/ different graphs. This is in sharp contrast to most other such constructions (including the de Bruijn graph), in which only one graph exists for each N. It is also shown how to implement certain algorithms on these networks.

[1] A. V. Aho and M. J. Corasick, "Efficient string matching: An aid to bibliographic search,"Commun. ACM, pp. 333-340, June 1975.
[2] S. B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to then-cube," inProc. Int. Conf. Parallel Processing, Aug. 1987, pp. 393-400.
[3] S. B. Akers and B. Krishnamurthy, "Group graphs as interconnection networks," inProc. 14th Int. Conf. Fault Tolerant Comput. Syst., June 1984, pp. 422-427.
[4] A.-H. Esfahanian and S. L. Hakimi, "Fault-tolerant routing in de Bruijn communications networks,"IEEE Trans. Comput., vol. C-34, pp. 777-788, Sept. 1985.
[5] M. A. Fiol, J. L. A. Yebra, and I. Miquel, "Line digraph iterations and the (d, k)-digraph problem,"IEEE Trans. Comput., vol. C-33, pp. 400-403, May 1984.
[6] H. Fredricksen, "A survey of full length nonlinear shift-register cycle algorithms,"SIAM Rev., vol. 24, pp. 195-221, Apr. 1982.
[7] R. L. Hemminger and L. W. Beineke, "Line graphs and line digraphs," inSelected Topics in Graph Theory, L. W. Beineke, Ed. New York: Academic, 1978.
[8] J. E. Hopcroft and J. D. Ullman,Introduction to Automata Theory, Languages, and Computation. Reading, MA: Addison-Wesley, 1979.
[9] M. Imase and M. Itoh, "A design for directed graphs with minimum diameter,"IEEE Trans. Comput., vol. C-32, pp. 782-784, Sept. 1983.
[10] M. Imase and M. Itoh, "Design to minimize diameter on building-block network,"IEEE Trans. Comput., vol. C-30, pp. 439-443, June 1981.
[11] M. Imase, T. Soneoka, and K. Okada, "Connectivity of regular directed graphs with small diameter,"IEEE Trans. Comput., vol. C-34, pp. 267-273, Mar. 1985.
[12] D. E. Knuth, J. H. Morris, and V. R. Pratt, "Fast pattern matching in strings,"SIAM J. Comput., vol. 6, pp. 323-350, June 1977.
[13] C. W. H. Lam and J. H. van Lint, "Directed graphs with unique paths of fixed lengths,"J. Combinatorial Theory, vol. B-24, pp. 331-337, 1978.
[14] A. Lempel, "On a homomorphism of the de Bruijn graph and its applications to the design of feedback shift registers,"IEEE Trans. Comput., vol. C-12, pp. 1204-1209, Dec. 1970.
[15] N. S. Mendelsohn, "Directed graphs with the unique path property," inCombinatorial Mathematics and its Applications, P. Erdos, A. Renyi and V. T. Sos, Eds., 1969.
[16] R. Y. Pinter, "Efficient string matching with don't-care patterns," inCombinatorial Algorithms on Words, A. Apostolico and Z. Galil, Eds., NATO ASI Series, Springer-Verlag, 1985, pp. 11-29.
[17] D. K. Pradhan, "Fault-tolerant multiprocessor link and bus network architectures,"IEEE Trans. Comput., vol. C-34, pp. 33-45, Jan. 1985.
[18] D. K. Pradhan and S. M. Reddy, "A fault-tolerant communication architecture for distributed systems,"IEEE Trans. Comput., vol. C-31, pp. 863-870, Sept. 1982.
[19] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[20] A. Sengupta, A. Sen, and S. Bandyopadhyay, "Fault-tolerant distributed system design,"IEEE Trans. Circuits Syst., vol. CAS-35, pp. 168-172, Feb. 1988.
[21] A. Sengupta, A. Sen, and S. Bandyopadhyay, "On an optimally fault tolerant multiprocessor network architecture,"IEEE Trans. Comput., vol. C-36, pp. 619-623, May 1987.
[22] M. A. Sridhar, "On the connectivity of the de Bruijn graph,"Inform. Proc. Lett., vol. 27, pp. 315-318, May 1988.
[23] M. A. Sridhar and C. S. Raghavendra, "Uniform minimal full-access networks,"J. Parallel Distributed Comput., vol. 5, pp. 383-403, 1988.
[24] M. A. Sridhar, "Updating the Aho-Corasick pattern matching machine,"Int. J. Comput. Math., to be published.

Index Terms:
fault tolerant networks; de Bruijn graph; directed graphs; vertices; node faults; fault-free diameter; hop; algorithm theory; directed graphs; fault tolerant computing.
M.A. Sridhar, C.S. Raghavendra, "Fault-Tolerant Networks Based on the de Bruijn Graph," IEEE Transactions on Computers, vol. 40, no. 10, pp. 1167-1174, Oct. 1991, doi:10.1109/12.93750
Usage of this product signifies your acceptance of the Terms of Use.