Self-stabilizing local mutual exclusion and daemon refinement

Abstract

Refining self-stabilizing algorithms which use tighter scheduling constraints (weaker daemon) into corresponding algorithms for weaker or no scheduling constraints (stronger daemon), while preserving the stabilization property, is useful and challenging. Designing transformation techniques for these refinements has been the subject of serious investigations in recent years. This paper proposes a transformation technique to achieve the above task. The heart of the transformer is a self- stabilizing local mutual exclusion algorithm. The local mutual exclusion problem is to grant a process the privilege to enter the critical section if and only if none of the neighbors of the process has the privilege. The contribution of this paper is twofold. First, we present a bounded-memory self-stabilizing local mutual exclusion algorithm for arbitrary network, assuming any arbitrary daemon. After stabilization, this algorithm maintains a bound on the service time (the delay between two successive executions of the critical section by a particular process). This bound is (formula presented) where n is the network size. Second, we use the local mutual exclusion algorithm to design two scheduler transformers which convert the algorithms working under a weaker daemon to ones which work under the distributed, arbitrary (or unfair) daemon, both transformers preserving the self-stabilizing property. The first transformer refines algorithms written under the central daemon, while the second transformer refines algorithms designed for the fc-fair (k > (n - 1)) daemon.