ABSTRACT
We study the problem of extending a circulant digraph network by adding spare nodes and extra links to make it fault-tolerant. The optimization criterion used is to reduce the node-degree of the overall network. Our formulation can tolerate any desired number of node failures; and moreover, it can be applied to networks whose edges are directed or undirected. Our results show the solutions obtained are efficient.
- Anderson, T., and P. Lee, "Fault-Tolerance Principles and Practice", Prentice-Hall International, London, 1981.Google Scholar
- Bermond, J., F. Comellas and D. Hsu, "Distributed Loop Computer Networks: A Survey", J. of Parallel and Dist. Computing, 24, 1995, pp. 2--10. Google ScholarDigital Library
- Bruck, J., R. Cypher and C. Ho, "Fault-Tolerant Meshes and Hypercubes With Minimal Number of Spares", IEEE Trans on Comp, 42, no. 9, September 1992, pp. 1089--1103. Google ScholarDigital Library
- Choudum, A., and S. Sivagurunathan, "Optimal fault-tolerant networks with a server", in Netowrks, V. 35, N. 2, Mar 2000, pp. 157-=160.Google Scholar
- Chuang, Y., L. Hsu and C. Chang, "Optimal 1-edge Fault-Tolerant Designs for Ladders", Info. Proc. Letters, 84, no. 2, October 2002, pp. 87--92. Google ScholarDigital Library
- Chung, F., F. Leighton, and A. Rosenberg, "Diogenes: a Methodology for Designing Fault-Tolerant VLSI Processor Arrays", in Proc. IEEE 13th Conf on Fault Tolerant Computing Symp, June 1993, Chicago, IL, pp. 26--32.Google Scholar
- Dawson, R. and A. Farrag, "Fault-tolerant Extensions of Star Networks," in Networks, V. 21, July 1991, pp. 373--385.Google ScholarCross Ref
- Dutt, S., and J. Hayes, "Designing Fault-Tolerant Systems Using Automorphisms", J. on Parallel and Dist Computing, 12, no. 3, July 1991, pp. 249--268. Google ScholarDigital Library
- Farrag, A., "Algorithm for Constructing Fault-Tolerant Solutions of the Circulant Graph Configuration", in Proc. of 5th IEEE Symp. on Frontiers of Massively Parallel Computations, February 1995, McLean, Virginia, pp. 514--520. Google ScholarDigital Library
- Farrag, A., "Developing Fault-Tolerant Distributed Loops", Information Processing Letters, V. 111, N. 2, December 2010, pp. 97--101. Google ScholarDigital Library
- Farrag, A., "Extending a Distributed Loop Network to Tolerate Node Failures", in ACM Proc. of Parallel & Dist Testing and Debugging Workshop of the ISSTA Symposium, July 2011, Toronto, Ontario, Canada, pp. 45--51. Google ScholarDigital Library
- Farrag, A., and S. Lou, "Applying Fault-Tolerant Solutions of Circulant Graphs to Multi-Dimensional Meshes" in Computers & Mathematics Journal, 50, no. 8--9, November 2005, pp. 1383--1394. Google ScholarDigital Library
- Farrag, A., S. Lou and Y. Qi, "Fault-tolerance and Reconfiguration of Circulant Graphs and Hypercubes", in Proc. of High Performance Computing Symposium (HPCS-08), Ottawa, Ontario, Canada, Apr 2008, pp. 475--481. Google ScholarDigital Library
- Grnanov, A., L. Kleinrock, and M. Gerla, "A highly Reliable Distributed Loop Network Architecture", in Proc. IEEE Symp. Fault Tolerant Computing, Kyoto, Japan, Oct 1980, pp. 319--324.Google Scholar
- Hoffman, A., "On the polynomial of a graph", The Amer. Math. Monthly, V. 70, N. 1, Jan 1963, pp. 30--36.Google ScholarCross Ref
- Hoffman, A., and M. McAndrew, "The polynomial of a directed graph", Proc. Amer. Math. Soc., V. 16, N.2, Apr 1965, pp. 303--309.Google ScholarCross Ref
- Lipson, J., "Elements of Algebra and Algebraic Computing", Benjamin/Cummings Publisher, Melno Park, California, 1981.Google Scholar
- Liu, M. T., "distributed Loop Computer Networks", Advances in Computers, Vol. 17, Academic Press, New York, 1978, pp. 163--221.Google Scholar
- Peha, J., and F. Toubagi, "Analyzing the Fault Tolerance of Double-Loop Networks", IEEE/ACM Trans. on Networking, V. 2, N. 4, August 1994, pp. 363--373. Google ScholarDigital Library
- Raghavendra, C., M. Gerla and A. Avizienis, "A Reliable Loop topologies for Large Local Computer Networks", IEEE Trans. Computer, V. 34, N. 1, Jan 1985, pp. 46--55. Google ScholarDigital Library
- Raghavendra, C., and J. Silvester, "Double Loop Network Architectures - A Performance Study", IEEE Trans. Comm., V. 33, N. 2, Feb 1985, pp. 185--187.Google ScholarCross Ref
- Rennels, D., "On Implementing Fault-Tolerance in Binary Hypercubes", Digest of papers of IEEE Symp on Fault-Tolerant Comp, (July), Vienna, Austria, 344--349.Google Scholar
- Schmitter, E., and P. Baues, "The Basic Fault-Tolerant System", IEEE Micro, 4, no. 1, February 1984, pp. 66--74. Google ScholarDigital Library
- Snyder, L., "Introduction to the Configurable, Highly Parallel Computer," IEEE Computer, 15, no. 1, January 1992, pp. 47--56. Google ScholarDigital Library
- Sung, T., M. Lin, and T. Ho, "Multiple-Edge-Fault Tolerance with respect to Hypercubes", IEEE Trans. Parallel and Dist Systems, 8, no. 2, February 1997, pp. 187--192. Google ScholarDigital Library
Index Terms
- Fault-tolerant circulant digraphs networks
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