Revisiting Randomized Parallel Load Balancing Algorithms

  • Guy Even
  • Moti Medina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)


We deal with the well studied allocation problem of assigning n balls to n bins so that the maximum number of balls assigned to the same bin is minimized. We focus on randomized, constant-round, distributed, asynchronous algorithms for this problem.

Adler et al. [1] presented lower bounds and upper bounds for this problem. A similar lower bound appears in Berenbrink et al. [2]. The lower bound is based on a topological assumption. Our first contribution is the observation that the topological assumption does not hold for two algorithms presented by Adler et al. [1]. We amend this situation by presenting direct proofs of the lower bound for these two algorithms.

We present an algorithm in which a ball that was not allocated in the first round retries with a new choice in the second round. We present tight bounds on the maximum load obtained by our algorithm. The analysis is based on analyzing the expectation and transforming it to a bound with high probability using martingale tail inequalities.

Finally, we present a 3-round heuristic with a single synchronization point. We conducted experiments that demonstrate its advantage over parallel algorithms for 106 ≤ n ≤ 108 balls and bins. In fact, the obtained maximum load meets the best results for sequential algorithms.


static randomized parallel allocation load balancing balls and bins martingales 


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  1. 1.
    Adler, M., Chakrabarti, S., Mitzenmacher, M., Rasmussen, L.E.: Parallel randomized load balancing. Random Struct. Algorithms 13(2), 159–188 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Berenbrink, P., auf der Heide, F.M., Schröder, K.: Allocating Weighted Jobs in Parallel. Theory of Computing Systems 32(3), 281–300 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Azar, Y., Broder, A., Karlin, A., Upfal, E.: Balanced allocations. SIAM journal on computing 29(1), 180–200 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Stemann, V.: Parallel balanced allocations. In: Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures, pp. 261–269. ACM, New York (1996)Google Scholar
  5. 5.
    Czumaj, A., auf der Heide, F., Stemann, V.: Contention Resolution in Hashing Based Shared Memory Simulations. SIAM Journal On Computing 29(5), 1703–1739 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Voecking, B.: How Asymmetry Helps Load Balancing. Journal of the ACM 50(4), 568–589 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, Cambridge (2005)CrossRefzbMATHGoogle Scholar
  8. 8.
    Kolchin, V., Sevastyanov, B., Chistyakov, V.: Random Allocations. John Wiley & Sons, Chichester (1978)Google Scholar
  9. 9.
    Raab, M., Steger, A.: ”Balls into bins” - a simple and tight analysis. In: Rolim, J.D.P., Serna, M., Luby, M. (eds.) RANDOM 1998. LNCS, vol. 1518, pp. 159–170. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Guy Even
    • 1
  • Moti Medina
    • 1
  1. 1.School of Electrical EngineeringTel-Aviv Univ.Tel-AvivIsrael

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