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Composite k-Arbiters
November 2001 (vol. 12 no. 11)
pp. 1134-1145

Abstract—The k-Arbiter is a useful concept to solve the distributed h-out-of-k mutual exclusion problem. The distributed h-out-of-k mutual exclusion algorithms, based on the k-arbiter, have the benefits of high fault tolerance and low message cost. However, according to the definition of the k-arbiter, it is required to have a nonempty intersection among any (k+1) quorums in a k-arbiter. Consequently, constructing k-arbiters is difficult. The coterie join operation proposed by Neilsen and Mizuno produces a new and larger coterie by joining known coteries. In this paper, by extending the coterie join operation, we first propose a k-arbiter join operation to construct a new and larger k-arbiter from known k-arbiters for a large system. Then, we derive a necessary and sufficient condition for the k-arbiter join operation to construct a nondominated joined k-arbiter. Moreover, we discuss availability properties of the joined k-arbiters. We observe that, by selecting proper k-arbiters, the joined k-arbiter can provide a higher availability than that of the original input. Finally, we propose a k-arbiter compound operation to construct k-arbiters by using coteries and/or k-coteries. By that way, the problem of constructing k-arbiters can be reduced to the problem of constructing coteries and/or k-coteries.

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Index Terms:
Distributed systems, fault tolerance, h-out-of-k mutual exclusion, permission-based algorithms, quorums.
Yu-Chen Kuo, "Composite k-Arbiters," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 11, pp. 1134-1145, Nov. 2001, doi:10.1109/71.969124
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