2007 **Abstract:** We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol…

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“…In such a situation the collision probability (i.e. the probability of two nodes choosing the same ID) is given by the birthday paradox p(X(n t )) = 1 − 16 ), in which X is a discrete uniform distribution of IDs and n t is the total number of nodes deployed. As it can be seen in Figure 1, the collision probability is over 10% with only 120 nodes, and reaches 50% with ∼ 300 nodes.…”

confidence: 99%

“…In such a situation the collision probability (i.e. the probability of two nodes choosing the same ID) is given by the birthday paradox p(X(n t )) = 1 − 16 ), in which X is a discrete uniform distribution of IDs and n t is the total number of nodes deployed. As it can be seen in Figure 1, the collision probability is over 10% with only 120 nodes, and reaches 50% with ∼ 300 nodes.…”

confidence: 99%

“…We have a much more relaxed goal. We want to find a 2-distance graph coloring with a minimum number of messages, bounded by a maximum of 2 16 colors.…”

confidence: 99%

“…Angluin, Aspnes, Fischer and Jiang [2] construct a self-stabilizing leader election algorithm for anonymous, unidirectional, asynchronous rings of odd size in the framework of their model of population protocols. Beauquier, Gradinariu and Johnen [5] present a randomized self-stabilizing leader election algorithm under an arbitrary scheduler (no fairness assumption is required) on anonymous, unidirectional rings of known size, in the shared variables model. Both algorithms are based on token circulation.…”

mentioning

confidence: 99%