, Volume 5, Issue 1–4, pp 243–250 | Cite as

An optimal time bound for oblivious routing

  • Ian Parberry


The problem of routing data packets in a constant-degree network is considered. A routing scheme is calledoblivious if the route taken by each packet is uniquely determined by its source and destination. The time required for the oblivious routing ofn packets onn processors is known to be Θ(√n). It is demonstrated that the presence of extra processors can expedite oblivious routing. More specifically, the time required for the oblivious routing ofn packets onp processors is Θ(n/√p + logn).

Key words

Normal algorithm Oblivious Parallel computation Routing Shuffle-exchange 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Borodin and J. E. Hopcroft, Routing, merging and sorting on parallel models of computation,Proc. 14th Ann. ACM Symp. on Theory of Computing, San Francisco, CA, May 1982.Google Scholar
  2. [2]
    L. M. Goldschlager, A universal interconnection pattern for parallel computers,J. Assoc. Comput. Mach., vol. 29, no. 4, pp. 1073–1086, Oct. 1982.MATHMathSciNetGoogle Scholar
  3. [3]
    A. Gottlieb, R. Grishman, C. P. Kruskal, K. P. McAuliffe, L. Rudolph, and M. Snir, The NYU ultracomputer-designing an MIMD shared memory parallel computer,IEEE Trans. Comput., vol. 32, no. 2, Feb. 1983.Google Scholar
  4. [4]
    T. Lang, Interconnections between processors and memory modules using the shuffle-exchange network,IEEE Trans. Comput., vol. 25, no. 5, May 1976.Google Scholar
  5. [5]
    D. Nassimi and S. Sahni, Data broadcasting in SIMD computers,IEEE Trans. Comput., vol. 30, no. 2, pp. 101–106, Feb. 1981.MathSciNetGoogle Scholar
  6. [6]
    D. Nassimi and S. Sahni, Parallel permutation and sorting algorithms and a new generalized connection network,J. Assoc. Comput. Mach., vol. 29, no. 3, pp. 642–667, July 1982.MATHMathSciNetGoogle Scholar
  7. [7]
    I. Parberry, A complexity theory of parallel computation, PH.D. Thesis, Department of Computer Science, University of Warwick, May 1984.Google Scholar
  8. [8]
    I. Parberry, On recurrent and recursive interconnection patterns,Inform. Process. Lett., vol. 22, no. 6, pp. 285–289, May 1986.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    I. Parberry,Parallel Complexity Theory, Research Notes in Theoretical Computer Science, Pitman, London, 1987.Google Scholar
  10. [10]
    I. Parberry, Some practical simulations of impractical parallel computers,Parallel Comput., vol. 4, no. 1, pp, 93–101, Feb. 1987.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    F. P. Preparata and J. Vuillemin, The cube-connected cycles: a versatile network for parallel computation,Comm. ACM, vol. 24, no. 5, pp. 300–309, May 1981.CrossRefMathSciNetGoogle Scholar
  12. [12]
    C. L. Seitz, The cosmic cube,Comm. ACM, vol. 28, no. 1, pp. 22–23, Jan. 1985.CrossRefMathSciNetGoogle Scholar
  13. [13]
    H. S. Stone, Parallel processing with the perfect shuffle,IEEE Trans. Comput., vol. 20, no. 2, pp. 153–161, Feb. 1971.MATHCrossRefGoogle Scholar
  14. [14]
    J. D. Ullman,Computational Aspects of VLSI, Computer Science Press, Rockville, MD, 1984.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Ian Parberry
    • 1
  1. 1.Department of Computer Science, Whitmore LaboratoryThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations