Advertisement

Competitive source routing on tori and meshes

  • Tzuoo-Hawn Yeh
  • heng-Ming Kuo
  • Chin-Laung Lei
  • Hsu-Chun Yen
Session 2B
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1350)

Abstract

We study the source routing problem onN x √N tori and meshes. In this problem, the paths for packets are the shortest ones. And the routing decision is distributed in a way that the path designated to a packet is determined entirely on its source node, with no knowledge of the other packets injected to other nodes and the system load distribution. The cost we concern about is the maximum load among the edges. We use competitive analysis to measure the performance of algorithms. We show that the competitive ratio for any algorithm is ,Ω(log N), and we provide an algorithm whose competitive ratio is O(log N).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Alon, G. Kalai, M. Ricklin, and L. Stockmeyer. Lower bounds on the competitive ratio for mobile user tracking and distributed job scheduling. In 33rd FOCS, pages 334–343, 992.Google Scholar
  2. 2.
    B. Awerbuch, Y. Azar, and S. Plotkin. Throughput-competitive online routing. In 34th FOGS, pages 32–40, 1993.Google Scholar
  3. 3.
    B. Awerbuch, Y. Bartal, and A. Fiat. Competitive distributed file allocation. In 25th STOC, pages 164–173, 1993.Google Scholar
  4. 4.
    B. Awerbuch, Y. Bartal, A. Fiat, and A. Rosen. Competitive non-preemptive call control. In 5th SODA, pages 312–320, 1994.Google Scholar
  5. 5.
    B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani. On-line admission control and circuit routing for high performance computing and communication. In 35th FOCS, pages 412–423, 1994.Google Scholar
  6. 6.
    B. Awerbuch, S. Kutten, and D. Peleg. Competitive distributed job scheduling. In 24th STOC, pages 517–580, 1992.Google Scholar
  7. 7.
    Y. Bartal, A. Fiat, and Y. Rabani. Competitive algorithms for distributed data management. In 24th STOC, pages 39–50, 1992.Google Scholar
  8. 8.
    Y. Banal and A. Rosén. The distributed k-server problem — a competitive distributed translator for k-server algorithms. In 33rd FOGS, pages 344–353, 1992.Google Scholar
  9. 9.
    A. Borodin, P. Raghavan, B. Schieber, and E. Upfal. How much can hardware help routing. In 25th STOC, pages 573–582, 1993.Google Scholar
  10. 10.
    S. Irani, N. Reingold, J. Westbrook, and D. Sleator. Randomized competitive algorithms for the list update problem. In 2nd SODA, pages 251–260, 1991.Google Scholar
  11. 11.
    C. Kaklamanis, D. Krizanc, and T. Tsantilas. Tight bounds for oblivious routing in the hypercube. In 2nd SPAA, pages 31–36, 1990.Google Scholar
  12. 12.
    E. Koutsoupias and C. Papadimitriou. On the k-server conjecture. In 26th STOC, pages 507–511, 1994.Google Scholar
  13. 13.
    M. Kunde. Packet routing on grids of processors. Algorithmica, 9(1):32–46, 1993.Google Scholar
  14. 14.
    T. Leighton. Average case analysis of greedy routing algorithms on arrays. In 2nd SPAA, pages 2–10, 1990.Google Scholar
  15. 15.
    T. Leighton, F. Makedon, and I. Tollis. A 2n −2 step algorithm for routing in an nx n array with constant size queues. In 1st SPAA, pages 328–335, 1989.Google Scholar
  16. 16.
    S. Rajasekaran and R. Overholt. Constant queue routing on a mesh. In 8th Annual Symposium on Theoretical Aspects of Computer Science, volume 480 of Lecture Nodes in Computer Science, pages 444–455, Springer-Verlag, 1991.Google Scholar
  17. 17.
    J. Sibeyn, B. Chlebus, and M. Kaufmann. Deterministic permutation routing on meshes. J. Algorithms, 22:111–141, 1997.Google Scholar
  18. 18.
    D. Sleator and R. Tarjan. Amortized efficiency of list update and paging rules. Comm. ACM, 28:202–208, 1985.Google Scholar
  19. 19.
    S. Vishwanathan. Randomized on-line graph coloring. J. Algorithms, 13(4):657–669, 1992.Google Scholar
  20. 20.
    T.-H. Yeh, C.-M. Kuo, C.-L. Lei, and H.-C. Yen. Competitive source routing on tori and meshes. Technical report, Dept. of Electrical Engineering, National Taiwan University, 1996.Google Scholar
  21. 21.
    N. Young. The k-server dual and loose competitiveness for paging. Algorithmica, 11(6):525–541, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Tzuoo-Hawn Yeh
    • 1
  • heng-Ming Kuo
    • 1
  • Chin-Laung Lei
    • 1
  • Hsu-Chun Yen
    • 1
  1. 1.Department of Electrical EngineeringNational Taiwan UniversityTaiwanROC

Personalised recommendations