Self-stabilizing Leader Election in Population Protocols over Arbitrary Communication Graphs

This paper considers the fundamental problem of

self-stabilizing leader election

(

$\mathcal{SSLE}$

) in the model of

population protocols

. In this model, an unknown number of asynchronous, anonymous and finite state mobile agents interact in pairs over a given communication graph.

$\mathcal{SSLE}$

has been shown to be impossible in the original model. This impossibility can been circumvented by a modular technique augmenting the system with an

oracle

- an external module abstracting the added assumption about the system. Fischer and Jiang have proposed solutions to

$\mathcal{SSLE}$

, for complete communication graphs and rings, using an oracle Ω?, called the

eventual leader detector

. In this work, we present a solution for arbitrary graphs, using a

composition

of two copies of Ω?. We also prove that the difficulty comes from the requirement of self-stabilization, by giving a solution without oracle for arbitrary graphs, when an uniform initialization is allowed. Finally, we prove that there is no self-stabilizing

implementation

of Ω? using

$\mathcal{SSLE}$

, in a sense we define precisely.