Composite k-arbiters

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 (κ + 1) quorums in a k-arbiter. Consequently, constructing k-arbiters is difficult. The coterie join operation proposed by Neilsen and Mizuno (1992) produces a new and larger coterie by joining known coteries. 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