Byzantine and Multi-writer K-Quorums

  • Amitanand S. Aiyer
  • Lorenzo Alvisi
  • Rida A. Bazzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4167)


Single-writer k-quorum protocols achieve high availability without incurring the risk of read operations returning arbitrarily stale values: in particular, they guarantee that, even in the presence of an adversarial scheduler, any read operation will return the value written by one of the last k writes. In this paper, we expand our understanding of k-quorums in two directions: first, we present a single-writer k-quorum protocol that tolerates Byzantine server failures; second, we extend the single-writer k-quorum protocol to a multi-writer solution that applies to both the benign and Byzantine cases. For a system with m writers, we prove a lower bound of \({\big( (2m-1)(k-1) + 1 \big)}\) on the staleness of any multi-writer protocol built over a single-writer k-quorum system and propose a multi-writer protocol that provides an almost matching staleness bound of \({\big( (2m-1)(k-1) + m \big)}\).


Read Operation Mean Time Between Failure Quorum System Probabilistic Construction Byzantine Fault 
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  1. 1.
    Raynal, M., Beeson, D.: Algorithms for mutual exclusion. MIT Press, Cambridge (1986)MATHGoogle Scholar
  2. 2.
    Castro, M., Liskov, B.: Practical byzantine fault tolerance. In: Proc. of the Third Symposium on Operating Systems Design and Implementation. USENIX Association, Co-sponsored by IEEE TCOS and ACM SIGOPS (1999)Google Scholar
  3. 3.
    Susan Davidson, H.G.M., Skeen, D.: Consistency in partioned network. Computing Survey 17(3) (1985)Google Scholar
  4. 4.
    Herlihy, M.: Replication methods for abstract data types. Technical Report TR-319. MIT/LCS (1984)Google Scholar
  5. 5.
    Naor, M., Wool, A.: The load, capacity, and availability of quorum systems. SIAM Journal on Computing 27(2), 423–447 (1998)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Peleg, D., Wool, A.: The availability of quorum systems. Inf. Comput. 123(2), 210–223 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Malkhi, D., Reiter, M.K., Wool, A., Wright, R.N.: Probabilistic quorum systems. Inf. Comput. 170(2), 184–206 (2001)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Yu, H.: Signed quorum systems. In: Proc. 23rd PODC, pp. 246–255. ACM Press, New York (2004)Google Scholar
  9. 9.
    Aiyer, A.S., Alvisi, L., Bazzi, R.A.: On the availability of non-strict quorum systems. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 48–62. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Lamport, L.: On interprocess communication. part i: Basic formalism. Distributed Computing 1(2), 77–101 (1986)MATHCrossRefGoogle Scholar
  11. 11.
    Martin, J.P., Alvisi, L., Dahlin, M.: Minimal byzantine storage. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 311–325. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Aiyer, A., Alvisi, L., Bazzi, R.A.: Byzantine and multi-writer k-quorums. Number TR-06-37 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Amitanand S. Aiyer
    • 1
  • Lorenzo Alvisi
    • 1
  • Rida A. Bazzi
    • 2
  1. 1.Department of Computer SciencesThe University of Texas at Austin 
  2. 2.Computer Science and Engineering DepartmentArizona State University 

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