Self-stabilizing Mutual Exclusion and Group Mutual Exclusion for Population Protocols with Covering

Joffroy Beauquier (1, 2) , Janna Burman (1, 2, 3)

1 LRI - Laboratoire de Recherche en Informatique
2 GRAND-LARGE - Global parallel and distributed computing
3 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications

This paper presents and proves correct two self-stabilizing deterministic algorithms solving the mutual exclusion and the group mutual exclusion problems in the model of population protocols with covering. In this variant of the population protocol model, a local fairness is used and bounded state anonymous mobile agents interact in pairs according to constraints expressed in terms of their cover times. The cover time is an indicator of the "time" for an agent to communicate with all the other agents. This indicator is expressed in the number of the pairwise communications (events) and is unknown to agents. In the model, we also assume the existence of a particular agent, the base station. In contrast with the other agents, it has a memory size proportional to the number of the agents. We prove that without this kind of assumption, the mutual exclusion problem has no solution. The algorithms in the paper use a phase clock tool. This is a synchronization tool that was recently proposed in the model we use. For our needs, we extend the functionality of this tool to support also phases with unbounded (but finite) duration. This extension seems to be useful also in the future works.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Joffroy Beauquier, Janna Burman. Self-stabilizing Mutual Exclusion and Group Mutual Exclusion for Population Protocols with Covering. 15th International Conference On Principles Of Distributed Systems, OPODIS 2011, Dec 2011, Toulouse, France. ⟨hal-00639651⟩