Synchronous Byzantine quorum systems

Quorum systems have been used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. Malkhi and Reiter recently proposed quorum systems that can tolerate Byzantine failures; they called these systems Byzantine quorum systems and gave some examples of such quorum systems. In this paper, we propose a new definition of Byzantine quorums that is appropriate for synchronous systems. We show how these quorums can be used for data replication and propose a general construction of synchronous Byzantine quorums using standard quorum systems. We prove tight lower bounds on the load of synchronous Byzantine quorums for various patterns of failures and we present synchronous Byzantine quorums that have optimal loads that match the lower bounds for two failure patterns.

[1]  David K. Gifford,et al.  Weighted voting for replicated data , 1979, SOSP '79.

[2]  Toshihide Ibaraki,et al.  A Theory of Coteries: Mutual Exclusion in Distributed Systems , 1993, IEEE Trans. Parallel Distributed Syst..

[3]  Akhil Kumar,et al.  Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data , 1991, IEEE Trans. Computers.

[4]  Divyakant Agrawal,et al.  An efficient and fault-tolerant solution for distributed mutual exclusion , 1991, TOCS.

[5]  David Peleg,et al.  Crumbling Walls: A Class of Practical and Efficient Quorum Systems (Extended Abstract) , 1995, PODC.

[6]  David Peleg,et al.  The Availability of Quorum Systems , 1995, Inf. Comput..

[7]  Rida A. Bazzi,et al.  Planar quorums , 1996, Theor. Comput. Sci..

[8]  Michael K. Reiter,et al.  Byzantine quorum systems , 1997, STOC '97.

[9]  Michael Rabinovich,et al.  A performance study of general grid structures for replicated data , 1993, [1993] Proceedings. The 13th International Conference on Distributed Computing Systems.

[10]  Ozalp Babaoglu,et al.  Proceedings of the 10th International Workshop on Distributed Algorithms , 1996 .

[11]  M. Mizuno,et al.  Decentralized consensus protocols , 1991, [1991 Proceedings] Tenth Annual International Phoenix Conference on Computers and Communications.

[12]  David Peleg,et al.  How to be an efficient snoop, or the probe complexity of quorum systems (extended abstract) , 1996, PODC '96.

[13]  M. P. Herlihy.  REPLICATION METHODS FOR ABSTRACT DATA TYPES , 1984 .

[14]  Avishai Wool,et al.  The load and availability of Byzantine quorum systems , 1997, PODC '97.

[15]  Moni Naor,et al.  The Load, Capacity, and Availability of Quorum Systems , 1998, SIAM J. Comput..

[16]  Dale Skeen,et al.  A Quorum-Based Commit Protocol , 1982, Berkeley Workshop.

[17]  Mitchell L. Neilsen,et al.  Quorum structures in distributed systems , 1992 .

[18]  D. Peleg,et al.  Crumbling Walls: A Class of High Availability Quorum Systems , 1994, PODC 1994.

[19]  Hector Garcia-Molina,et al.  How to assign votes in a distributed system , 1985, JACM.

[20]  Mamoru Maekawa,et al.  A N algorithm for mutual exclusion in decentralized systems , 1985, TOCS.