<p><b>Abstract</b>—We model a distributed system by a graph <tmath>$G=(V,E)$</tmath>, where <tmath>$V$</tmath> represents the set of processes and <tmath>$E$</tmath> the set of bidirectional communication links between two processes. <tmath>$G$</tmath> may not be complete. A popular (distributed) mutual exclusion algorithm on <tmath>$G$</tmath> uses a coterie <tmath>${\cal C} (\subseteq 2^V)$</tmath>, which is a nonempty set of nonempty subsets of <tmath>$V$</tmath> (called quorums) such that, for any two quorums <tmath>$P, Q \in {\cal C}$</tmath>, 1) <tmath>$P \cap Q \ne \emptyset$</tmath> and 2) <tmath>$P \not\subset Q$</tmath> 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.</p>
Availability, coteries, distributed systems, $G$-nondominatedness, graph theory, mutual exclusion problems, quorums.