Transversal merge operation: a nondominated coterie construction method for distributed mutual exclusion

A coterie is a set of subsets (called quorums) of the processes in a distributed system such that any two quorums intersect with each other and is mainly used to solve the mutual exclusion problem in a quorum-based algorithm. The choice of a coterie sensitively affects the performance of the algorithm and it is known that nondominated (ND) coteries achieve good performance in terms of criteria such as availability and load. On the other hand, grid coteries have some other attractive features: 1) a quorum size is small, which implies a low message complexity, and 2) a quorum is constructible on the fly, which benefits a low space complexity. However, they are not ND coteries unfortunately. To construct ND coteries having the favorite features of grid coteries, we introduce the transversal merge operation that transforms a dominated coterie into an ND coterie and apply it to grid coteries. We call the constructed ND coteries ND grid coteries. These ND grid coteries have availability higher than the original ones, inheriting the above desirable features from them. To demonstrate this fact, we then investigate their quorum size, load, and availability, and propose a dynamic quorum construction algorithm for an ND grid coterie.