Planar quorums

Quorum systems are used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failures. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system. c © 2000 Elsevier Science B.V. All rights reserved.

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

[2]  Toshihide Ibaraki,et al.  Optimal coteries for rings and related networks , 1992, [1992] Proceedings of the 12th International Conference on Distributed Computing Systems.

[3]  Robert H. Thomas,et al.  A Majority consensus approach to concurrency control for multiple copy databases , 1979, ACM Trans. Database Syst..

[4]  David Peleg,et al.  Crumbling walls: a class of practical and efficient quorum systems , 1995, PODC '95.

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

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

[7]  Cheng-Hong Cho,et al.  Triangular Grid Protocol: An Efficient Scheme for Replica Control with Uniform Access Quorums , 1996, Euro-Par, Vol. II.

[8]  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.

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

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

[11]  Ye-In Chang,et al.  A fault-tolerant triangular mesh protocol for distributed mutual exclusion , 1995, Proceedings.Seventh IEEE Symposium on Parallel and Distributed Processing.

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

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

[16]  Chienwen Wu,et al.  The triangular lattice protocol: a highly fault tolerant and highly efficient protocol for replicated data , 1992, [1992] Proceedings 11th Symposium on Reliable Distributed Systems.

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

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

[19]  Masaaki Mizuno,et al.  Coterie Join Algorithm , 1992, IEEE Trans. Parallel Distributed Syst..

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

[21]  John Sheehan,et al.  GRAPH THEORY: AN INTRODUCTORY COURSE (Springer Graduate Texts in Mathematics) , 1980 .

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