Self-stabilizing depth-first token passing on rooted networks

Abstract

We present a deterministic distributed depth-first token passing protocol on a rooted network. This protocol does not use either the processor identifiers or the size of the network, 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 reach a state with no more than one token in the network. The protocol implements a strictly fair token circulation—during a round, every processor obtains the token exactly once. The proposed protocol has extremely small memory requirement—only O(1) bits of memory per incident network link.