Self-stabilization
Spanders: Distributed spanning expanders
Science of Computer Programming
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A self-stabilizing algorithm [2] is a distributed algorithm with an additional property: it guarantees to eventually execute its task, by reaching a legitimate configuration , regardless of the state in which the processes and communication links are started. Some algorithms are supposed to remain safe at all times while they carry out their task. Safety, however, is impossible when very high levels of failures overwhelm the system, e.g., when more than a third of the processes are Byzantine, or in the extreme case, when all the processes disappear.