Fast consensus in networks of bounded degree

  • Piotr Berman
  • Juan A. Garay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 486)

Abstract

In a Distributed Consensus protocol all processors (of which t may be faulty) are given (binary) initial values; after exchanging messages all correct processors must agree on one of them. In this paper we focus on consensus in networks that are not completely interconnected, following the work of Dwork et al. [DPPU]. In such a context, complete consensus among all the correct processors is not possible and some exceptions must be allowed.

We first show how to achieve consensus in the butterfly network using O (t+logn loglogn) one bit parallel transmission steps, while tolerating the asymptotically optimal number of faulty processors and asymptotically minimal number of exceptions. This result considerably improves upon our previous protocol, in particular it replaces the running time of O (n logn loglogn) with an asymptotically optimal one. As in [DPPU], we can decrease the number of exceptions to O(t) by using additional links, while maintaining the same running time.

The protocol is derived from a consensus protocol for complete networks that is interesting in its own right. It achieves Distributed Consensus with optimal number of processors, asymptotically optimal total bit transfer and nearly optimal number of rounds, with better constant factors than previously published results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B]
    B. Bollobás, "Random Graphs," combinatorics, London Math. Society LN 52, Cambridge University Press, 1981, pp. 80–102.Google Scholar
  2. [BD]
    A. Bar-Noy and D. Dolev, "Families of Consensus Algorithms," Proc. 3rd Aegean Workshop on Computing, June/July 1988, pp. 380–390.Google Scholar
  3. [BDDS]
    A. Bar-Noy, D. Dolev, C. Dwork and H.R. Strong, "Shifting gears: changing algorithms on the fly to expedite Byzantine Agreement," Proc. 6th PODC, August 1987, pp. 42–51.Google Scholar
  4. [BG]
    P. Berman and J.A. Garay, "Asymptotically Optimal Distributed Consensus," Proc. ICALP 89, LNCS, Vol. 372, July 1989, pp. 80–94.Google Scholar
  5. [BGP1]
    P. Berman, J.A. Garay and K.J. Perry, "Towards Optimal Distributed Consensus," Proc. 30th FOCS, October 1989, pp. 410–415.Google Scholar
  6. [BGP2]
    P. Berman, J.A. Garay and K.J. Perry, "Recursive Phase King Protocols for Distributed Consensus," PSU, CS Dept. Tech Report CS-89-24, August 1989.Google Scholar
  7. [CASD]
    F. Cristian, H. Aghili, R. Strong and D. Dolev, "Atomic Broadcast: From Simple Message Diffusion to Byzantine Agreement," Proc. 15th Inernational Symp. on Fault-Tolerant Computing, June 1985, pp. 200–206. Revised version in IBM research report RJ5244.Google Scholar
  8. [CW1]
    B. Coan and J.Welch, "Modular Construction of Nearly Optimal Byzantine Agreement Protocols," Proc. 9th Annual PODC, August 1989, pp. 295–306.Google Scholar
  9. [CW2]
    B. Coan and J. Welch, "A Byzantine Agreement Protocol with Optimal Message Bit Complexity," Proc. 27th Annual Allerton Conf. on Communication, Control and Computing, 1989.Google Scholar
  10. [D]
    D. Dolev, "The Byzantine generals strike again," Journal of Algorithms, Vol. 3, No. 1 (1982), pp. 14–30.Google Scholar
  11. [DPPU]
    C. Dwork, D. Peleg, N. Pippenger and E. Upfal, "Fault Tolerance in Networks of Bounded Degree," Proc. 18th STOC, May 1986, pp. 370–379.Google Scholar
  12. [DR]
    D. Dolev and R. Reischuk, "Bounds of Information Exchange for Byzantine Agreement," JACM, Vol. 32, No. 1, (1985), pp. 191–204.Google Scholar
  13. [DS]
    D. Dolev and H.R. Strong, "Polynomial Algorithms for Multiple Processor Agreement," Proc. 14th STOC, May 1982, pp. 401–407.Google Scholar
  14. [FM]
    P. Feldman and S. Micali, "Optimal Algorithms for Byzantine Agreement," Proc. 20th STOC, May 1988, pp. 148–161.Google Scholar
  15. [LSP]
    L. Lamport, R.E. Shostak and M. Pease, "The Byzantine Generals Problem," ACM ToPLaS, Vol. 4, No. 3, July 1982, pp. 382–401.Google Scholar
  16. [MW]
    Y. Moses and O. Waarts, "Coordinated Traversal: (t+1)-Round Byzantine Agreement in Polynomial Time," Proc. 29th FOCS, October 1988, pp. 246–255.Google Scholar
  17. [P]
    N. Pippinger, "On Networks of Noisy Gates," Proc. 26th FOCS, October 1985, pp. 31–38.Google Scholar
  18. [U]
    J.D. Ullman, "Computational Aspects of VLSI," Computer Science Press, 1984.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Piotr Berman
    • 1
  • Juan A. Garay
    • 2
  1. 1.Department of Computer ScienceThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

Personalised recommendations