Self-Stabilizing Local Mutual Exclusion and Daemon Refinement

Abstract

Refining self-stabilizing algorithms which use tighter schedul- ing constraints (weaker daemon) into corresponding algorithms for weak- er or no scheduling constraints (stronger daemon), while preserving the stabilization property, is useful and challenging. Designing transforma- tion techniques for these refinements has been the subject of serious in- vestigations in recent years. This paper proposes a transformation tech- nique 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 con- tribution 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 main- tains a bound on the service time (the delay between two successive ex- ecutions of the critical section by a particular process). This bound is nx(n-1)/2where n is the network size. Second, we use the local mutual ex- clusion 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 preserv- ing 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.