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Coterie Join Algorithm
September 1992 (vol. 3 no. 5)
pp. 582-590
Given a set of nodes in a distributed system, a coterie is a collection of subsets of the set of nodes such that any two subsets have a non empty intersection and are not properly contained in one another. A subset of nodes in a coterie is called a quorum. An algorithm, called the join algorithm, which takes nonempty coteries as input, and returns a new, larger coterie called a composite coterie is introduced. It is proved that a composite coterie is nondominated if and only if the input coteries are nondominated.Using the algorithm, dominated or nondominated coteries may be easily constructed for a large number of nodes. An efficient method for determining whether a given set of nodes contains a quorum of a composite coterie is presented. As an example, tree coteries are generalized using the join algorithm, and it is proved that tree coteries are nondominated. It is shown that the join algorithm may be used to generate read and write quorums which may be used by a replica control protocol.

[1] D. Agrawal and A. El Abbadi, "An efficient and fault-tolerant algorithm for distributed mutual exclusion," inProc. Eight Annu. ACM Symp. Principles Distributed Comput., 1989.
[2] D. Agrawal and A. El Abbadi, "Exploiting logical structures in replicated databases,"Inform. Processing Lett., vol. 33, pp. 255-260, 1990.
[3] D. Barbara and H. Garcia-Molina, "The vulnerability of vote assignments,"ACM Trans. Comput. Syst., vol. 4, no. 3, pp. 187-213, 1986.
[4] D. Barbara and H. Garcia-Molina, "Mutual exclusion in partitioned distributed systems,"Distributed Comput., vol. 1, pp. 119-132, 1986.
[5] P.A. Bernstein, V. Hadzilacos, and N. Goodman,Concurrency Control and Recovery in Database Systems, Addison-Wesley, Reading, Mass., 1987.
[6] H. Garcia-Molina and D. Barbara, "How to assign votes in a distributed systems,"J. ACM, vol. 32, no. 4, pp. 841-860, Oct. 1985.
[7] D. Gifford, "Weighted voting for replicated data," inProc. 7th ACM Symp. Oper. Syst. Principles, Dec. 1979, pp. 150-162.
[8] M. P. Herlihy, "A quorum-consensus replication method for abstract data types,"ACM Trans. Comput. Syst., vol. 4, no. 1, Feb. 1986.
[9] L. Lamport, "Time, clocks, and the ordering of events in a distributed system,"Commun. ACM, vol. 21, no. 7, pp. 558-565, July 1978.
[10] M. Maekawa, "A√N algorithm for mutual exclusion in decentralized systems,"ACM Trans. Comput. Syst., vol. 3, no. 2, May 1985.

Index Terms:
Index Termsdistributed system; nonempty intersection; nonempty coteries; composite coterie; treecoteries; join algorithm; read and write quorums; replica control protocol; distributedalgorithms; trees (mathematics)
M.L. Nielsen, M. Mizuno, "Coterie Join Algorithm," IEEE Transactions on Parallel and Distributed Systems, vol. 3, no. 5, pp. 582-590, Sept. 1992, doi:10.1109/71.159041
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