Tight Bounds for Selfish and Greedy Load Balancing

  • Ioannis Caragiannis
  • Michele Flammini
  • Christos Kaklamanis
  • Panagiotis Kanellopoulos
  • Luca Moscardelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)

Abstract

We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it selects to run its job to the server among its permissible servers having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness.

We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy and price of stability of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling. In: Proc. of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1997), pp. 493–500 (1997)Google Scholar
  2. 2.
    Avidor, A., Azar, Y., Sgall, J.: Ancient and new algorithms for load balancing in the L p norm. Algorithmica 441, 422–441 (2001)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Awerbuch, B., Azar, Y., Grove, E.F., Kao, M.-Y., Krishnan, P., Vitter, J.S.: Load balancing in the L p norm. In: Proc. of the 36th Annual Symposium on Foundations of Computer Science (FOCS 1995), pp. 383–391 (1995)Google Scholar
  4. 4.
    Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 57–66 (2005)Google Scholar
  5. 5.
    Azar, Y., Epstein, A.: Convex programming for scheduling unrelated parallel machines. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 331-337 (2005)Google Scholar
  6. 6.
    Chandra, A.K., Wong, C.K.: Worst-case analysis of a placement algorithm related to storage allocation. SIAM Journal on Computing 4(3), 249–263 (1975)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 67-73 (2005)Google Scholar
  8. 8.
    Christodoulou, G., Koutsoupias, E.: On the price of anarchy and stability of correlated equilibria of linear congestion games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Cody, R.A., Coffman, E.G.: Record allocation for minimizing expected retrieval costs on drum-like storage devices. Journal of the ACM 115, 103–115 (1976)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 413–420 (2002)Google Scholar
  11. 11.
    Fabrikant, A., Papadimitriou, C., Talwar, K.: On the complexity of pure equilibria. In: Proc. of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), pp. 604–612 (2004)Google Scholar
  12. 12.
    Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The structure and complexity of Nash equilibria for a selfish routing game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 123–134. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 593–605. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: Computing Nash equilibria for scheduling on restricted parallel links. In: Proc. of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), pp. 613-622 (2004)Google Scholar
  15. 15.
    Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate equilibria and ball fusion. Theory of Computing Systems 36(6), 683–693 (2003)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 547–558. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Mavronicolas, M., Spirakis, P.: The price of selfish routing. In: Proc. of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 510–519 (2001)Google Scholar
  19. 19.
    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Papadimitriou, C.: Algorithms, games and the internet. In: Proc. of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 749–753 (2001)Google Scholar
  21. 21.
    Phillips, S., Westbrook, J.: Online load balancing and network flow. In: Proc. of the 25th Annual ACM Symposium on Theory of Computing (STOC 1993), pp. 402–411 (1993)Google Scholar
  22. 22.
    Rosenthal, R.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Roughgarden, T., Tardos, E.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games and Economic Behavior 47(2), 389–403 (2004)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Shmoys, D., Wein, J., Williamson, D.: Scheduling parallel machines on-line. SIAM Journal on Computing 24(6), 1313–1331 (1995)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Suri, S., Tóth, C., Zhou, Y.: Selfish load balancing and atomic congestion games. In: Proc. of the 16th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2004), pp. 188–195 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ioannis Caragiannis
    • 1
  • Michele Flammini
    • 2
  • Christos Kaklamanis
    • 1
  • Panagiotis Kanellopoulos
    • 1
  • Luca Moscardelli
    • 2
  1. 1.Research Academic Computer Technology Institute and Dept. of Computer Engineering and InformaticsUniversity of PatrasRioGreece
  2. 2.Dipartimento di InformaticaUniversità di L’ AquilaL’ AquilaItaly

Personalised recommendations