Self-stabilizing Leader Election in Networks of Finite-state Anonymous Agents

Abstract

This paper considers the self-stabilizing leader-election problem in a model of interacting anonymous finite-state agents. Leader election is a fundamental problem in distributed systems; many distributed problems are easily solved with the help of a central coordinator. Self-stabilizing algorithms do not require initialization in order to operate correctly and can recover from transient faults that obliterate all state information in the system. Anonymous finite-state agents model systems of identical simple computational nodes such as sensor networks and biological computers. Self-stabilizing leader election is easily shown to be impossible in such systems without additional structure.

An eventual leader detector $\Omega?$ is an oracle that eventually detects the presence or absence of a leader. With the help of $\Omega?$, uniform self-stabilizing leader election algorithms are presented for two natural classes of network graphs: complete graphs and rings. The first algorithm works under either a local or global fairness condition, whereas the second requires global fairness. With only local fairness, uniform self-stabilizing leader election in rings is impossible, even with the help of $\Omega?$.

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