Advertisement

Packet routing on grids of processors

  • Manfred Kunde
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 401)

Abstract

The problem of packet routing on n1 × ... × n r mesh-connected arrays or grids of processors is studied. For two-dimensional grids a deterministic routing algorithm is given for n × n meshes where each processor has a buffer of size f(n)<n It needs 2n+O(n/f(n)) steps on grids without wrap-arounds. Hence it is asymptotically optimal and as good as randomized algorithms routing data only with high probability. Furthermore it is demonstrated that on r-dimensional cubes of processors packet routing can be performed by asymptotically (2r − 2)n steps which is faster than the running times of so far known randomized algorithms and of deterministic algorithms.

Keywords

Buffer Size Correction Phase Deterministic Algorithm Sorting Algorithm Additional Buffer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [KRT]
    Krizanc, D.,Rajasekaran, S., Tsantilas, Th.: Optimal routing algorithms for mesh-connected processor arrays. Proceedings AWOC'88.In: Reif, J.H. (ed.),Lect. Notes Comp. Sci.,vol 319,pp. 411–422,Berlin:Springer 1988Google Scholar
  2. [KT]
    Kunde, M., Tensi, T.: Multi-packet-routing on mesh connected arrays. To appear in: Proceedings of ACM Symposium on Parallel Algorithms and Architectures SPAA89, June 1989.Google Scholar
  3. [Ku1]
    Kunde, M.: Lower bounds for sorting on mesh-connected architectures. Acta Informatica 24, 121–130 (1987).MathSciNetGoogle Scholar
  4. [Ku2]
    Kunde, M.: Optimal sorting on multi-dimensionally mesh-connected computers. Proceedings of STACS 87. In: Brandenburg, F.J., et al. (eds.), Lect. Notes Comp. Sci., vol. 247, pp. 408–419, Berlin: Springer 1987Google Scholar
  5. [Ku3]
    Kunde, M.: Bounds for l-section and related problems on grids of processors. Proceedings of PARCELLA 88. In: Wolf, G., Legendi, T., Schendel, U. (eds.), Mathematical Research, vol. 48, pp. 298–307, Akademie Verlag, Berlin, 1988Google Scholar
  6. [Ku4]
    Kunde, M.: Routing and Sorting on Mesh-Connected Arrays. Proceedings AWOC'88. In: Reif, J.H. (ed.),Lect. Notes Comp. Sci.,vol 319,pp. 423–433,Berlin:Springer 1988Google Scholar
  7. [LMT]
    Leighton, T., Makedon, F., Tollis, I.G.: A 2n − 2 algorithm for routing in an n × n array with constant size queues. To appear in: Proceedings of ACM Symposium on Parallel Algorithms and Architectures SPAA89, June 1989.Google Scholar
  8. [MSS]
    Ma, Y., Sen, S., Scherson, I.D.: The distance bound for sorting on mesh-connected processor arrays is tight. Proceedings FOCS 86, pp. 255–263Google Scholar
  9. [RT]
    Rajasekaran, S., Tsantilas, Th.: An optimal randomized routing algorithm for the mesh and a class of efficient mesh-like routing networks. 7th Conf. on Found. of Software Technology and Theoret. Comp. Science, Pune, 1987, pp. 226–241Google Scholar
  10. [SS]
    Schnorr, C.P., Shamir, A.: An optimal sorting algorithm for mesh-connected computers, pp. 255–263. Proceedings STOC 1986. Berkley 1986Google Scholar
  11. [TK]
    Thompson, C.D., Kung, H.T.: Sorting on a mesh-connected parallel computer. CACM 20, 263–271 (1977)Google Scholar
  12. [VB]
    Valiant, L.G., Brebner, G.J.: Universal schemes for parallel communication. Proceedings STOC 81, pp. 263–277.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Manfred Kunde
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2West Germany

Personalised recommendations