Skip to main content
SpringerLink
Log in
Book cover

European Dependable Computing Conference

EDCC 1994: Dependable Computing — EDCC-1 pp 529–545Cite as

Reconfiguration of faulty hypercubes

  • Session 12: Switching networks and hypercubes
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 852))

Abstract

The problem of tolerating faulty nodes in hypercubes has been studied by many researchers either by using spares or by reconfiguration. In this paper, an algorithm for tolerating faulty nodes in hypercubes is presented. The algorithm is based on using general spanning trees for reconfiguring the hypercube to avoid faulty nodes. The algorithm contains two phases: the first phase involves the construction of the spanning tree, and the second one is for reconfiguring the hypercube should a faulty node be detected. The reconfiguration process introduced consists of two basic steps. First, the faulty node is disconnected from the spanning tree. Then, a new spanning tree is constructed by reconnecting the children of the faulty node to the spanning tree. This paper deals with reconfiguring faulty hypercubes; however, the same algorithm can be generalized to work for reconfiguration of multicomputer networks in general in the presence of faults. Single fault coverage of 100% and almost 100% fault coverage of double and triple faults are achieved by the proposed algorithm, with no extra-dilation for hypercubes having a dimension of n≥ 10. Simulation results for the algorithm under more than three faults also are presented. Fault coverage and congestion results for up to 60 faults having different cube sizes are discussed.

Research supported in part by NSF and by the Texas Advanced Technology Program under grant no. 999903-029.

This author is supported by King Fahd Univ. of Petroleum and Minerals, Saudi Arabia, Dhahran 31261

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Altawil, D. Avresky, and D. Pradhan, “Fault Tolerance of Hypercubes Using Spanning Trees,” Technical Report 93-055, Department of Computer Science, Texas A & M University, Dec. 93.

    Google Scholar 

  2. K.M. Altawil and D.R. Avresky, “Reconfiguration of Spanning Trees in Faulty Hypercubes,” Proc. 23rd Int'l Con. on Par. Proc., Chicago, Illinois, USA, Aug. 1994.

    Google Scholar 

  3. D.R. Avresky et al., “An Approach to Fault Diagnosis in Multimicrocomputer Systems: Algorithm and Simulation,” Proc. 17th Int'l Symp. on Fault Tolerant Computing, pp. 305–310, June 1987.

    Google Scholar 

  4. S.G. Aki, The Design and Analysis of Parallel Algorithms. Prentice-Hall International, Inc., 1989.

    Google Scholar 

  5. A. Bagchi and S. Hakimi, “Data Transfers in Broadcast Networks,” IEEE Trans. on Comp., Vol. C-41, No. 7, July 1992, pp. 842–847.

    Article  Google Scholar 

  6. P. Banerjee, “Strategies for Reconfiguring Hypercubes Under Faults,” Proc. 20th Int'l Symp. on Fault Tolerant Computing. pp. 210–217, June 1990.

    Google Scholar 

  7. J. L. Bentley, “A Parallel Algorithm for Constructing Minimum Spanning Trees,” J. of Algorithms, Vol. 1, No. 1, pp. 51–59, March 1980.

    Article  Google Scholar 

  8. A. Bagchi, S. Hakimi, J. Mitchem, and E. Schmeichel, “Parallel Algorithms For Gossiping by Mail,” Information Processing Letters, Vol. 34, pp. 197–202, April 1990.

    Article  Google Scholar 

  9. D. Bertsekas, C. Ozveren, G. Stamoulis, P. Tseng, and J. Tsitsiklis, “Optimal Communication Algorithms for Hypercubes,” J. of Par. and Dist. Computing, Vol 11, pp. 263–275, 1991.

    Article  Google Scholar 

  10. T. Cormen, C. Leiserson, and R. Rivest, Introduction to Algorithms. McGraw-Hill, pp. 498–513, 1990.

    Google Scholar 

  11. M. Y. Chen and S. Lee, “Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes,” IEEE Tran. on Par. and Dist. Sys., Vol. 4, No. 3, March 1993.

    Google Scholar 

  12. S. Chau and A. Liestman, “A Proposal for a Fault Tolerant Binary Hypercube Architecture,” Proc. 19th Int'l Symp. on Fault Tolerant Computing, pp. 323–330, June 1989.

    Google Scholar 

  13. S. Dutt and J. Hayes, “An Automorphic Approach to the design of Fault-Tolerant Multiprocessors,” Proc. 19th Int'l Symp. on Fault Tolerant Computing, pp. 496–503, June 1989.

    Google Scholar 

  14. Kemal Efe and Kumar Ramaiyer, “Congestion and Fault Tolerance of Binary Tree Embeddings on Hypercube,” Fifth Int'l. Par. Proc. Symp., 1991.

    Google Scholar 

  15. G. Frederickson, “Data Structures for On-Line Updating of Minimum Spanning Trees with Applications,” SIAM J. Comput, Vol 14, No 4, Nov. 1985.

    Google Scholar 

  16. R. Gallager, P. Humblet, and P. Spira, “A Distributed Algorithm for Minimum Weight Spanning Trees,” ACM Trans. on Prog. Languages and Systems. Vol. 5, No. 1, pp. 66–77, Jan. 1983.

    Article  Google Scholar 

  17. S. Johnsson, and C. Ho, “Optimum Broadcasting and Personalized Communication in Hypercubes,” IEEE Trans. on Comp., Vol. C-38, No. 9, pp. 197–202, Sept. 1989.

    Google Scholar 

  18. S. Kwan and W Ruzzo. “Adaptive Parallel Algorithms for Finding Minimum Spanning Trees,” Proc, of the 1984 Int'l. Conf. on Parallel Processing, Bellaire, Michigan, pp. 439–443, Aug. 1984.

    Google Scholar 

  19. T. Lee and J. Hayes, “Design of Gracefully Degradable Hypercube-Connected Systems,” J. of Parallel and Distributed Computing, Vol. 14, pp. 390–401, 1992.

    Article  Google Scholar 

  20. M. Peercy and P. Banerjee, “Distributed Algorithms for Shortest-Path, Deadlock-Free Routing and Broadcasting in Arbitrarily Faulty Hypercubes,” Proc. 20th Int'l Symp. on Fault Tolerant Computing, pp. 218–225, June 1990.

    Google Scholar 

  21. S. Ravindran and A. Gibbons, “Dense Edge-Disjoint Embedding of Complete Binary Trees in the Hypercube,” Information Processing Letters. Vol. 45, pp. 321–325, April 1993.

    Article  Google Scholar 

  22. D. Rennets, “On Implementing Fault Tolerance in Binary Hypercubes,” Proc. 16th Int'l Symp. on Fault Tolerant Computing, pp. 344–349, June 1986.

    Google Scholar 

  23. K. Ravindran, G. Sing, and P. Gupta, “Reconfiguration of Spanning Trees in Networks in the Presence of Node Failures,” The 13th Int'l. Conf. on Distr. Comp. Sys., pp. 219–226. May 1993.

    Google Scholar 

  24. C. Raghavendra, P. Yang, and S. Tien, “Free Dimensions — An Effective Approach to Achieving Fault Tolerance in Hypercubes,” Proc. 22nd Int'l Symp. on Fault Tolerant Computing, pp. 170–177, July 1992.

    Google Scholar 

  25. Y. Saad and M. Schultz, “Topological Properties of Hypercubes,” IEEE Tran. on Comp., Vol. C-37, No. 7, July 1988. pp. 867–872.

    Article  Google Scholar 

  26. A. Sen, A. Sengupta, and S. Bandyopadhyay, “On Some Topological Properties of Hypercube, Incomplete Hypercube and Supercube,” Seventh Int'l. Par. Proc. Symp., 1993.

    Google Scholar 

  27. G. Stamoulis and J. Tsitsiklis, “An Efficient Algorithm for Multiple Simultaneous Broadcasts in the Hypercube,” Information Processing Letters, Vol. 46, pp. 219–224. July 1993.

    MathSciNet  Google Scholar 

  28. G. Stamoulis and J. Tsitsiklis, “Efficient Routing Schemes for Multiple Broadcasts in Hypercubes,” IEEE Trans. on Par. and Dist. Sys., Vol. 4, No. 7, pp. 725–739, July 1993.

    Article  Google Scholar 

  29. A. Wagner, “Embedding All Binary Trees in the Hypercube,” J. of Par. and Dist. Computing, Vol. 18, pp. 33–43, 1993.

    Article  Google Scholar 

  30. F. Wang and F. Lin, “On Constructing Multiple Spanning Trees in a Hypercube,” Information Processing Letters, Vol. 45, pp. 177–183, March 1993.

    Article  Google Scholar 

  31. W.W. White, “Mapping General Trees and Graphs into the Hypercube,” Proc. of the ISCA Int'l. Conf., Parallel and Distributed Computing, pp. 157–161, October 14–16. 1993.

    Google Scholar 

  32. P. Yang and C. Raghavendra, “Embedding and Reconfiguration of Binary Trees in Faulty Hypercubes,” Sixth Int'l. Par. Proc. Symp., pp. 2–9, 1992.

    Google Scholar 

  33. P. Yang and C. Raghavendra, “Reconfiguration of Binary Trees in Faulty Hypercubes,” Seventh Int'l. Par. Proc. Symp., pp. 401–405, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, 77843-3112, College Station, TX

    Dimiter R. Avresky & Khalid M. Al-Tawil

Authors
  1. Dimiter R. Avresky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Khalid M. Al-Tawil
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Klaus Echtle Dieter Hammer David Powell

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Avresky, D.R., Al-Tawil, K.M. (1994). Reconfiguration of faulty hypercubes. In: Echtle, K., Hammer, D., Powell, D. (eds) Dependable Computing — EDCC-1. EDCC 1994. Lecture Notes in Computer Science, vol 852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58426-9_156

Download citation

  • DOI: https://doi.org/10.1007/3-540-58426-9_156

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58426-1

  • Online ISBN: 978-3-540-48785-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation