Fast Self-Stabilizing Depth-First Token Circulation

We present a simple deterministic distributed depth-first token circulation (DFTC) protocol for arbitrary rooted network. This protocol does not require processors to have identifiers, but assumes the existence of a distinguished processor, called the root of the network. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to converge to the intended behavior in finite time. The proposed protocol stabilizes in O(n) time units, i.e., no more than the time for the token to visit all the processors (in the depth-first search order). It compares very favorably with all previously published DFTC algorithms for arbitrary rooted networks--they all stabilize in O(n × D) times, where D is the diameter of the network.

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