Issue No. 11 - November (2001 vol. 12)

ISSN: 1045-9219

pp: 1134-1145

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.969124

ABSTRACT

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

INDEX TERMS

Distributed systems, fault tolerance, h-out-of-k mutual exclusion, permission-based algorithms, quorums.

CITATION

Y. Kuo, "Composite k-Arbiters," in

*IEEE Transactions on Parallel & Distributed Systems*, vol. 12, no. , pp. 1134-1145, 2001.

doi:10.1109/71.969124

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