Distributed Computing

, Volume 18, Issue 1, pp 85–98 | Cite as

The inherent price of indulgence

  • Partha Dutta
  • Rachid GuerraouiEmail author
Special Issue PODC


An indulgent algorithm is a distributed algorithm that tolerates asynchronous periods of the network when process crash detection is unreliable. This paper presents a tight bound on the time complexity of indulgent consensus algorithms.

We consider a round-based eventually synchronous model, and we show that any t-resilient consensus algorithm in this model, requires at least t+2 rounds for a global decision even in runs that are synchronous. We contrast our lower bound with the well-known t+1 round tight bound on consensus in the synchronous model. We then prove the bound to be tight by exhibiting a new t-resilient consensus algorithm in the eventually synchronous model that reaches a global decision at round t+2 in every synchronous run. Our new algorithm is in this sense significantly faster than the most efficient indulgent algorithm we know of, which requires 2t+2 rounds in synchronous runs.

Our lower bound applies to round-based consensus algorithms with unreliable failure detectors such as ⋄ P and ⋄ S, and our matching algorithm can be adapted to such failure detectors.


Fault tolerance Distributed algorithms Consensus time complexity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aguilera, M.K., Toueg, S.: A simple bivalency proof that t-resilient consensus requires t+1 rounds. Inform. Proces. Lett. 71(3-4), 155-158 (1999)MathSciNetGoogle Scholar
  2. 2.
    Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. J. ACM 43(2), 225-267 (1996)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Charron-Bost, B., Guerraoui, R., Schiper, A.: Synchronous system and perfect failure detector: solvability and efficiency issues. In: Proceedings of the IEEE International Conference on Dependable Systems and Networks (DSN), pp. 523-532 New York (2000)Google Scholar
  4. 4.
    Charron-Bost, B., Schiper, A.: Uniform consensus harder than consensus. DSC Technical Report 2000-28, Department of Communication Systems, Swiss Federal Institute of Technology, Lausanne (2000)Google Scholar
  5. 5.
    Dutta, P., Guerraoui, R., Pochon, B.: Tight bounds on early local decisions in uniform consensus. In: Proceedings of the 17th International Conference on Distributed Computing (DISC), Sorrento, Italy (2003)Google Scholar
  6. 6.
    Dwork, C., Lynch, N.A., Stockmeyer, L.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288-323 (1988)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374-382 (1985)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Gafni, E.: Round-by-round fault detectors: Unifying synchrony and asynchrony. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC-17), pp. 143-152 Puerto Vallarta, Mexico (1998)Google Scholar
  9. 9.
    Guerraoui, R.: Indulgent algorithms. In: Proceedings of the 19th ACM Symposium on Principles of Distributed Computing (PODC-19), pp. 289-298 Portland, OR (2000)Google Scholar
  10. 10.
    Hurfin, M., Raynal, M.: A simple and fast asynchronous consensus protocol based on a weak failure detector. Distribut. Comput. 12(4), 209-223 (1999)Google Scholar
  11. 11.
    Keidar, I., Rajsbaum, S.: A simple proof of the uniform consensus synchronous lower bound. Inform. Process. Lett. 85(1), 47-52 (2003); A preliminary version appeared in SIGACT News 32(2), 45-63 (2001)Google Scholar
  12. 12.
    Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. ACM Trans. Program. Languages Syst. 4(3), 382-401 (1982)Google Scholar
  13. 13.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann (1996)Google Scholar
  14. 14.
    Mostefaoui, A., Raynal, M.: Leader-based consensus. Parallel Proce. Lett. 11(1), 95-107 (2001)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Distributed Programming LaboratoryEPFLLausanneSwitzerland

Personalised recommendations