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Uniform Dynamic Self-Stabilizing Leader Election
April 1997 (vol. 8 no. 4)
pp. 424-440

Abstract—A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors exhibit a faulty behavior for a while and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next faulty period is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic self-stabilizing protocols for leader election under readwrite atomicity. Our protocols use randomization to break symmetry. The leader election protocol stabilizes in $O\left( {\Delta {\cal D}\log n} \right)$ time when the number of the processors is unknown and $O\left( {\Delta {\cal D}} \right),$ otherwise. Here Δ denotes the maximal degree of a node, ${\cal D}$ denotes the diameter of the graph and n denotes the number of processors in the graph. We introduce self-stabilizing protocols for synchronization that are used as building blocks by the leader-election algorithm. We conclude this work by presenting a simple, uniform, self-stabilizing ranking protocol.

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Index Terms:
Self-stabilizing systems, leader election, distributed algorithms, randomized distributed algorithms, synchronization.
Shlomi Dolev, Amos Israeli, Shlomo Moran, "Uniform Dynamic Self-Stabilizing Leader Election," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 4, pp. 424-440, April 1997, doi:10.1109/71.588622
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