On the Self-stabilization of Mobile Robots in Graphs

TL;DR

This paper introduces a new model for mobile robots in networks with transient faults, explores the possibility of self-stabilizing algorithms for naming and leader election, and provides solutions under minimal assumptions.

Contribution

It presents a novel model for mobile entities with path constraints, studies self-stabilizing algorithms for core problems, and offers solutions demonstrating problem equivalence.

Findings

Impossibility results for naming and leader election without constraints.

Deterministic and probabilistic solutions under minimal assumptions.

Equivalence of naming and leader election problems via reduction.

Abstract

Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The contribution of this paper is threefold. First, we present a new model for studying mobile entities in networks subject to transient faults. Our model differs from the classical robot model because robots have constraints about the paths they are allowed to follow, and from the classical agent model because the number of agents remains fixed throughout the execution of the protocol. Second, in this model, we study the possibility of designing self-stabilizing algorithms when those algorithms are run by mobile robots (or agents) evolving on a graph. We concentrate on the core building blocks of robot and agents problems: naming and leader election. Not surprisingly, when no constraints are given on the network graph topology and local execution model, both problems are impossible to solve. Finally, using minimal hypothesis with respect to impossibility results, we provide deterministic and probabilistic solutions to both problems, and show equivalence of these problems by an algorithmic reduction mechanism.