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Efficient Gossip and Robust Distributed Computation

  • Chryssis Georgiou
  • Dariusz R. Kowalski
  • Alex A. Shvartsman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2848)

Abstract

This paper presents an efficient deterministic gossip algorithm for p synchronous, crash-prone, message-passing processors. The algorithm has time complexity T = O(log2 p) and message complexity M=O(p 1 + ε), for any ε>0. This substantially improves the message complexity of the previous best algorithm that has M=O(p 1.77), while maintaining the same time complexity. The strength of the new algorithm is demonstrated by constructing a deterministic algorithm for performing n tasks in this distributed setting. Previous solutions used coordinator or check-pointing approaches, immediately incurring a work penalty Ω(n + f.p) for f crashes, or relied on strong communication primitives, such as reliable broadcast, or had work too close to the trivial Θ(p.n) bound of oblivious algorithms.The new algorithm uses p crash-prone processors to perform n similar and idempotent tasks so long as one processor remains active. The work of the algorithm is W = O(n + p.min{f + 1,log 3 p}) and its message complexity is M = O(fp ε  + pmin{f + 1, logp}), for any ε>0. This substantially improves the work complexity of previous solutions using simple point-to-point messaging, while “meeting or beating” the corresponding message complexity bounds. The new algorithms use communication graphs and permutations with certain combinatorial properties that are shown to exist. The algorithms are correct for any permutations, and in particular, the same expected bounds can be achieved using random permutations.

Keywords

Time Complexity Failure Pattern Communication Graph Message Complexity Work Complexity 
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.

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References

  1. 1.
    Alon, N., Spencer, J.H.: The Probabilistic Method, 2nd edn. J. Wiley and Sons, Inc., Chichester (2000)zbMATHCrossRefGoogle Scholar
  2. 2.
    Anderson, R.J., Woll, H.: Algorithms for the certified Write-All problem. SIAM Journal of Computing 26(5), 1277–1283 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chlebus, B., De Prisco, R., Shvartsman, A.A.: Performing tasks on restartable message-passing processors. Distributed Computing 14(1), 49–64 (2001)CrossRefGoogle Scholar
  4. 4.
    Chlebus, B.S., Gasieniec, L., Kowalski, D.R., Shvartsman, A.A.: Bounding work and communication in robust cooperative computation. In: 16th International Symposium on Distributed Computing, pp. 295–310 (2002)Google Scholar
  5. 5.
    Chlebus, B.S., Kowalski, D.R.: Gossiping to reach consensus. In: 14th Symposium on Parallel Algorithms and Architectures, pp. 220–229 (2002)Google Scholar
  6. 6.
    De Prisco, R., Mayer, A., Yung, M.: Time-optimal message-efficient work performance in the presence of faults. In: 13th Symposium on Principles of Distributed Computing, pp. 161–172 (1994)Google Scholar
  7. 7.
    Dwork, C., Halpern, J., Waarts, O.: Performing work efficiently in the presence of faults. SIAM Journal on Computing 27(5), 1457–1491 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Galil, Z., Mayer, A., Yung, M.: Resolving message complexity of byzantine agreement and beyond. In: 36th Symp. on Foundations of Comp. Sc., pp. 724–733 (1995)Google Scholar
  9. 9.
    Georgiou, C., Russell, A., Shvartsman, A.A.: The complexity of synchronous iterative Do-All with crashes. In: 15th Int-l Symposium on Distributed Computing, pp. 151–165 (2001)Google Scholar
  10. 10.
    Georgiou, C., Kowalski, D., Shvartsman, A.A.: Efficient gossip and robust distributed computation, http://www.engr.uconn.edu/~aas/GKS-2003.ps
  11. 11.
    Kanellakis, P.C., Shvartsman, A.A.: Efficient parallel algorithms can be made robust. Distributed Computing 5(4), 201–217 (1992)zbMATHCrossRefGoogle Scholar
  12. 12.
    Malewicz, G., Russell, A., Shvartsman, A.A.: Distributed cooperation during the absence of communication. In: 14th Int-l Symp. on Distr. Computing, pp. 119–133 (2000)Google Scholar
  13. 13.
    Pelc, A.: Fault-tolerant broadcasting and gossiping in communication networks. Networks 28, 143–156 (1996)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Chryssis Georgiou
    • 1
  • Dariusz R. Kowalski
    • 1
    • 2
  • Alex A. Shvartsman
    • 1
    • 3
  1. 1.Department of Computer Science and EngineeringUniversity of ConnecticutStorrsUSA
  2. 2.Instytut InformatykiUniwersytet WarszawskiWarsawPoland
  3. 3.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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