Nondominated Coteries on Graphs

Let C and D be two distinct coteries under the vertex set V of a graph G = (V, E) that models a distributed system. Coterie C is said to G-dominate D (with respect to G) if the following condition holds: For any connected subgraph H of G thatcontains a quorum in D (as a subset of its vertex set), there exists a connected subgraph H′ of H that contains a quorum in C. Acoterie C on a graph G is said to be G-nondominated (G-ND) (with respect to G) if no coterie D (≠ C) on G G-dominates C.Intuitively, a G-ND coterie consists of irreducible quorums. This paper characterizes G-ND coteries in graph theoretical terms, and presents a procedure for deciding whether or not a givencoterie C is G-ND with respect to a given graph G, based on this characterization. We then improve the time complexity of thedecision procedure, provided that the given coterie C is nondominated in the sense of Garcia-Molina and Barbara. Finally, wecharacterize the class of graphs G on which the majority coterie is G-ND

Improving the availability of mutual exclusion Systems on Incomplete Networks

We model a distributed system by a graph G=(V, E), where V represents the set of processes and E the set of bidirectional communication links between two processes. G may not be complete. A popular (distributed) mutual exclusion algorithm on G uses a coterie C(⊆2v), which is a nonempty set of nonempty subsets of V (called quorums) such that, for any two quorums P, Q ∈ C, 1) P∩Q ≠φ and 2) P￠Q hold. The availability is the probability that the algorithm tolerates process and/or link failures, given the probabilities that a process and a link, respectively, are operational. The availability depends on the coterie used in the algorithm. This paper proposes a method to improve the availability by transforming a given coterie