k-Arbiter Join Operation

k-Arbiter is a useful concept for solving the distributed h-out of-k resources allocation problem. The distributed h-out of-k resources allocation algorithms based on k-arbiter have the benefits of high fault-tolerance and low communication cost. However, according to the definition of k-arbiter, it is required to have a non-empty 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. Then, we derive a necessary and sufficient condition for the k-arbiter join operation to construct a nondominated composite k-arbiter. Moreover, we discuss the availability properties of the composite k-arbiters. We observe that by selecting the proper k-arbiters as join inputs, the composite k-arbiter can have a higher availability than that of the original inputs.