Leader Election for Anonymous Asynchronous Agents in Arbitrary Networks

TL;DR

This paper characterizes when and how leader election can be achieved among anonymous, asynchronous mobile agents in arbitrary unlabeled networks by exploiting initial position asymmetries and sharing information through meetings.

Contribution

It provides a complete characterization of initial configurations allowing leader election and presents an algorithm that works for all such configurations.

Findings

Identifies conditions under which leader election is possible in anonymous networks.

Develops an algorithm that guarantees leader election in all feasible configurations.

Provides a theoretical framework for leader election in asynchronous, anonymous agent systems.

Abstract

We study the problem of leader election among mobile agents operating in an arbitrary network modeled as an undirected graph. Nodes of the network are unlabeled and all agents are identical. Hence the only way to elect a leader among agents is by exploiting asymmetries in their initial positions in the graph. Agents do not know the graph or their positions in it, hence they must gain this knowledge by navigating in the graph and share it with other agents to accomplish leader election. This can be done using meetings of agents, which is difficult because of their asynchronous nature: an adversary has total control over the speed of agents. When can a leader be elected in this adversarial scenario and how to do it? We give a complete answer to this question by characterizing all initial configurations for which leader election is possible and by constructing an algorithm that accomplishes leader election for all configurations for which this can be done.