Self-stabilizing leader election in networks of finite-state anonymous agents

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?.