Obtaining nondominated k-coteries for fault-tolerant distributed k-mutual exclusion

A k-coterie is a family of sets (called quorums) in which any (k+1) quorums contain at least a pair of quorums intersecting each other. K-coteries can be used to develop distributed k-mutual exclusion algorithms that are resilient to node and/or communication link failures. A k-coterie is said to dominate another k-coterie if and only if every quorum in the latter is a super set of some quorum in the former. Obviously the dominating one has more chance than the dominated one for a quorum to be formed successfully in an error-prone environment. Thus, we should always concentrate on nondominated k-coteries that no k-coterie can dominate. We introduce a theorem for checking the nondomination of k-coteries, define a class of special nondominated k-coteries-strongly nondominated (SND) k-coteries, and propose two operations to generate new SND k-coteries from known SND k-coteries.