Skip to main content
SpringerLink
Log in

Robust algorithms for packet routing in a mesh

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

This paper considers the problem of permutation packet routing on a √n×√n mesh-connected array of processors. Each node in the array is assumed to be independently faulty with a probability bounded above by a valuep. This paper gives a routing algorithm which, ifp⩽ 0.29, will with very high probability route every packet that can be routed inO(√n logn) steps with queue lengths that areO(log2 n). Extensions to higher-dimensional meshes are given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations.Ann. of Math. Statist., 23:493–509, 1952.

    Google Scholar 

  2. J. Hastad, F. T. Leighton, and M. Newman. Reconfiguring a hypercube in the presence of faults.Proc. 19th Annual Symposium on Theory of Computing, pages 274–294, 1987.

  3. J. Hastad, F. T. Leighton, and M. Newman. Fast computation using faulty hypercubes.Proc. 21st Annual Symposium on Theory of Computing, pages 251–263, 1989.

  4. C. Kaklamanis, A. R. Karlin, F. T. Leighton, V. Milenkovic, P. Raghavan, S. Rao, C. D. Thomborson, and A. Tsantilas. Asymptotically tight bounds for computing with faulty arrays of processors.Proc. 31st Annual Symposium on Foundations of Computer Science, pages 285–296, 1990.

  5. F. T. Leighton and C. E. Leiserson, A survey of algorithms for integrating wafer-scale systolic arrays. InWafer Scale Integration, pages 177–195. Elsevier, Amsterdam, 1986.

    Google Scholar 

  6. F. T. Leighton and B. Maggs. Expanders might be practical: Fast algorithms for routing around faults in multibutterflies.Proc. 30th Annual Symposium on Foundations of Computer Science, pages 384–389, 1989.

  7. C. D. Thompson and H. T. Kung. Sorting on a mesh-connected parallel computer.Comm. ACM, 20:263–271, 1977.

    Google Scholar 

  8. E. Upfal. AnO(logN) deterministic packet routing scheme.Proc. 21st ACM Annual Symposium on Theory of Computing, pages 241–250, 1989.

  9. L. G. Valiant and G. J. Brebner. Universal schemes for parallel communication.Proc. 13th Annual ACM Symposium on Theory of Computing, pages 263–277, 1981.

Download references

Author information

Authors and Affiliations

  1. IBM Research Division, T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    P. Raghavan

Authors
  1. P. Raghavan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raghavan, P. Robust algorithms for packet routing in a mesh. Math. Systems Theory 28, 1–11 (1995). https://doi.org/10.1007/BF01294592

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01294592

Keywords

Search

Navigation