This Article 
 Bibliographic References 
 Add to: 
A Study of Odd Graphs as Fault-Tolerant Interconnection Networks
February 1991 (vol. 40 no. 2)
pp. 225-232

Odd graphs are analyzed to determine their suitable in designing interconnection networks. These networks are shown to possess many features that make them competitive with other architectures, such as ring, star, mesh, the binary n-cube and its generalized form, the chordal ring, and flip-trees. Among the features are small internode distances, a lighter density, simplicity in implementing various self-routing algorithms (both for faulty and nonfaulty networks), capability of maximal fault tolerance, strong resilience, and good persistence. The routing algorithms (both for the faulty and fault-free networks) do not require any table lookup mechanism, and intermediate nodes do not need to modify the message. These graphs are shown to have a partitioning property that is based on Hadamard matrices and can be effectively used for a system's expansion and self-diagnostics.

[1] 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.
[2] L. N. Bhuyan and D. P. Agarwal, "Design and performance of a general class of interconnection networks,"IEEE Trans. Comput., vol. C-30, pp. 587-590, Aug. 1981.
[3] S. B. Akers and B. Krishnamurthy, "Fault-tolerance in star graphs," inProc. 1987 Int. Conf. Supercomput., San Francisco, CA, May 1987.
[4] L. W. Hawkes, "A regular fault-tolerant architecture for interconnection networks,"IEEE Trans. Comput., vol. C-34, pp. 677-680, July 1985.
[5] 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.
[6] Q. F. Stout, "Mesh connected computers with broadcast,"IEEE Trans. Comput., vol. C-30, pp. 291-295, Apr. 1981.
[7] F. J. Meyer and D. K. Pradhan, "Flip-trees: Fault-tolerant graphs with wide containers,"IEEE Trans. Comput., vol. C-37, pp. 472-478, Apr. 1988.
[8] A. Ghafoor, T. R. Bashkow, and I. Ghafoor, "Bisectional fault-tolerant communication architecture for supercomputer systems,"IEEE Trans. Comput., vol. 38, pp. 1425-1446, Oct. 1989.
[9] F. P. Preparata, G. Metze, and R. T. Chien, "On the connection assignment problem of diagnosable systems,"IEEE Trans. Comput., pp. 848-854, Dec. 1967.
[10] J. G. Kuhl and S. M. Reddy, "Distributed fault-tolerance for large multiprocessor system," inProc. 1980 Comput. Architecture Conf., France, May 1980.
[11] N. Biggs, "Some odd graph theory,"Ann. NY Academy Sci., vol. 319, pp. 71-81, 1979.
[12] S. B. Akers and B. Krishnamurthy, "Group graphs as interconnection networks," inProc. 14th Int. Symp. Faul.-Tolerant Comput., Orlando, FL, June 1984, pp. 422-427.
[13] C. D. Godsil, "More odd graph theory,"Discrete Math., vol. 32, pp. 205-207, 1980.
[14] A. Ghafoor, "Some classes of fault-tolerant communication architecture for distributed computing systems," Tech. Rep. TR-85-4, Dep. Elec. Comput. Eng., Syracuse Univ., 1985.
[15] M. E. Watkins, "Connectivity in transitive graphs,"J. Combinatorial Theory, vol. 8, no. 1, pp. 23-29, Jan. 1970.
[16] F. J. MacWilliams and N. J. A. Sloane,The Theory of Error-Correcting Codes, Vols. I and II. New York: North-Holland, 1977.
[17] D. I. A. Cohen,Combinatorial Theory. New York: Wiley, 1978.

Index Terms:
odd graphs; fault-tolerant interconnection networks; ring; star; mesh; binary n-cube; chordal ring; flip-trees; self-routing algorithms; maximal fault tolerance; resilience; persistence; partitioning property; Hadamard matrices; self-diagnostics; fault tolerant computing; parallel architectures.
A. Ghafoor, T.R. Bashkow, "A Study of Odd Graphs as Fault-Tolerant Interconnection Networks," IEEE Transactions on Computers, vol. 40, no. 2, pp. 225-232, Feb. 1991, doi:10.1109/12.73594
Usage of this product signifies your acceptance of the Terms of Use.