Distributed Computing

, Volume 19, Issue 2, pp 104–125 | Cite as

Lower bounds for asynchronous consensus

  • Leslie Lamport
Original Article


Impossibility results and best-case lower bounds are proved for the number of message delays and the number of processes required to reach agreement in an asynchronous consensus algorithm that tolerates non-Byzantine failures. General algorithms exist that achieve these lower bounds in the normal case, when the response time of non-faulty processes and the transmission delay of messages they send to one another are bounded. Our theorems allow algorithms to do better in certain exceptional cases, and such algorithms are presented. Two of these exceptional algorithms may be of practical interest.


Consensus Fault tolerance Distributed algorithms Paxos 


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  1. 1.
    Brasileiro, F., Greve, F., Mostefaoui, A., Raynal, M.: Consensus in one communication step. In: Malyshkin, V. (ed.). Parallel Computing Technologies (6th International Conference, PaCT 2001), Lecture Notes in Computer Science, vol. 2127, pp. 42–50. Springer-Verlag (2001)MATHCrossRefGoogle Scholar
  2. 2.
    Charron-Bost, B., Schiper, A.: Uniform consensus is harder than consensus (extended abstract). Technical Report DSC/2000/028, école Polytechnique Fédérale de Lausanne, Switzerland (2000).
  3. 3.
    De Prisco, R., Lampson, B., Lynch, N.: Revisiting the paxos algorithm. Theor. Comput. Sci. 243:35–91 (2000)MATHCrossRefGoogle Scholar
  4. 4.
    Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288–323 (1988)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fischer, M.J., Lynch, N., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)MATHCrossRefGoogle Scholar
  7. 7.
    Lamport, L.: How to write a proof. American Mathematical Monthly 102(7):600–608 (1995)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Lamport, L.: The part-time parliament. ACM Trans. Comput. Syst. 16(2), 133–169 (1998)CrossRefGoogle Scholar
  9. 9.
    Lamport, L.: Paxos made simple. ACM SIGACT News (Distributed Computing Column) 32(4), 18–25 (2001)Google Scholar
  10. 10.
    Lamport, L.: Lower bounds for asynchronous consensus. In: Schiper, A., Shvartsman, A.A., Weatherspoon, H., Zhao, B.Y. (eds.). Future Directions in Distributed Computing, Lecture Notes in Computer Science, vol. 2584, pp. 22–23. Springer (2003)Google Scholar
  11. 11.
    Lamport, L.: Specifying Systems. Addison-Wesley, Boston (2003)Google Scholar
  12. 12.
    Lamport, L.: Fast paxos. Tech. Rep. MSR-TR-2005-112, Microsoft Research (2005)Google Scholar
  13. 13.
    Pedone, F., Schiper, A.: Handling message semantics with generic broadcast. Distributed Computing 15(2), 97–107 (2002)CrossRefGoogle Scholar
  14. 14.
    Wensley, J., et al.: SIFT: Design and analysis of a fault-tolerant computer for aircraft control. Proceedings of the IEEE 66(10), 1240–1254 (1978)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Leslie Lamport
    • 1
  1. 1.Microsoft Research Microsoft Corporation, One Microsoft WayRedmondUSA

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