Optimal Node Routing

  • Yossi Azar
  • Yoel Chaiutin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3884)

Abstract

We study route selection for packet switching in the competitive throughput model. In contrast to previous papers which considered competitive algorithms for packet scheduling, we consider the packet routing problem (output port selection in a node). We model the node routing problem as follows: a node has an arbitrary number of input ports and an arbitrary number of output queues. At each time unit, an arbitrary number of new packets may arrive, each packet is associated with a subset of the output ports (which correspond to the next edges on the allowed paths for the packet). Each output queue transmits packets in some arbitrary manner. Arrival and transmission are arbitrary and controlled by an adversary. The node routing algorithm has to route each packet to one of the allowed output ports, without exceeding the size of the queues. The goal is to maximize the number of the transmitted packets. In this paper, we show that all non-refusal algorithms are 2-competitive. Our main result is an almost optimal \(\frac{e}{e-1} \approx 1.58\)-competitive algorithm, for a large enough queue size. For packets with arbitrary values (allowing preemption) we present a 2-competitive algorithm for any queue size.

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References

  1. 1.
    Aiello, W., Kushilevitz, E., Ostrovsky, R.: Adaptive packet routing for bursty adversarial traffic. In: Proc. of the 30th ACM Symp. on Theory of Computing (STOC), pp. 359–368 (1998)Google Scholar
  2. 2.
    Aiello, W., Ostrovsky, R., Kushilevitz, E., Rosén, A.: Dynamic routing on networks with fixed-size buffers. In: Proc. 14th ACM-SIAM Symp. on Discrete Algorithms, pp. 771–780 (2003)Google Scholar
  3. 3.
    Ajtai, M., Aspnes, J., Naor, M., Rabani, Y., Schulman, L.J., Waarts, O.: Fairness in scheduling. Journal of Algorithms 29(2), 306–357 (1998)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Albers, S., Schmidt, M.: On the performance of greedy algorithms in packet buffering. In: Proc. 36th ACM Symp. on Theory of Computing, pp. 35–44 (2004)Google Scholar
  5. 5.
    Andrews, M., Awerbuch, B., Fernández, A., Kleinberg, J., Leighton, T., Liu, Z.: Universal stability results for greedy contention-resolution protocols. In: Proc. 37th IEEE Symp. on Found. of Comp. Science, pp. 380–389 (1996)Google Scholar
  6. 6.
    Awerbuch, B., Berenbrink, P., Brinkmann, A., Scheideler, C.: Simple online strategies for adversarial systems. In: Proc. of the 42nd IEEE Symp. on Foundation of Comupter Science (FOCS) (2001)Google Scholar
  7. 7.
    Awerbuch, B., Brinkmann, A., Scheideler, C.: Anycasting and multicasting in adversarial systems: Routing and admission control. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1153–1168. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Awerbuch, B., Leighton, F.: Improved approximation algorithms for the multi-commodity flow problem and local competitive routing in dynamic networks. In: Proc. of the 26th ACM Symp. on Theory of Computing (STOC), pp. 487–496 (1994)Google Scholar
  9. 9.
    Awerbuch, B., Mansour, Y., Shavit, N.: End-to-end communication with polynomial overhead. In: Proc. of the 30th IEEE Symp. on Foundation of Comupter Science (FOCS), pp. 358–363 (1989)Google Scholar
  10. 10.
    Azar, Y., Litichevskey, M.: Maximizing throughput in multi-queue switches. In: Proc. 12th Annual European Symposium on Algorithms, pp. 53–64 (2004)Google Scholar
  11. 11.
    Azar, Y., Richter, Y.: Management of multi-queue switches in QoS networks. In: Proc. 35th ACM Symp. on Theory of Computing, pp. 82–89 (2003)Google Scholar
  12. 12.
    Azar, Y., Richter, Y.: An improved algorithm for CIOQ switches. In: Proc. 12th Annual European Symposium on Algorithms, pp. 65–76 (2004)Google Scholar
  13. 13.
    Azar, Y., Richter, Y.: The zero-one principle for switching networks. In: Proc. 36th ACM Symp. on Theory of Computing, pp. 64–71 (2004)Google Scholar
  14. 14.
    Bansal, N., Fleischer, L., Kimbrel, T., Mahdian, M., Schieber, B., Sviridenko, M.: Further improvements in competitive guarantees for QoS buffering, pp. 196–207 (2004)Google Scholar
  15. 15.
    Birman, A., Gail, H.R., Hantler, S.L., Rosberg, Z., Sidi, M.: An optimal service policy for buffer systems. Journal of the Association Computing Machinery (JACM) 42(3), 641–657 (1995)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Borodin, A., Kleinberg, J., Raghavan, P., Sudan, M., Williamson, D.: Adversarial queuing theory. In: Proc. 28th ACM Symp. on Theory of Computing, pp. 376–385 (1996)Google Scholar
  17. 17.
    Gamarnik, D.: Stability of adaptive and non-adaptive packet routing policies in adversarial queueing networks. In: Proc. of the 31st ACM Symp. on Theory of Computing (STOC), pp. 206–214 (1999)Google Scholar
  18. 18.
    Karp, R., Vazirani, U., Vazirani, V.: An optimal algorithm for on-line bipartite matching. In: Proceedings of 22nd Annual ACM Symposium on Theory of Computing, May 1990, pp. 352–358 (1990)Google Scholar
  19. 19.
    Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B.: Buffer overflows of merging streams. In: Proc. 11th Annual European Symposium on Algorithms, pp. 349–360 (2003)Google Scholar
  20. 20.
    Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. In: Proc. 33rd ACM Symp. on Theory of Computing, pp. 520–529 (2001)Google Scholar
  21. 21.
    May, M., Bolot, J.C., Jean-Marie, A., Diot, C.: Simple performance models of differentiated services for the internet. In: Proceedings of the IEEE INFOCOM 1999, pp. 1385–1394 (1999)Google Scholar
  22. 22.
    Scheideler, C., Vocking, B.: From static to dynamic routing: efficient transformations of store-and-forward protocols. In: Proc. of the 31st ACM Symp. on Theory of Computing (STOC), pp. 215–224 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yossi Azar
    • 1
  • Yoel Chaiutin
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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