Self-stabilizing depth-first token circulation in arbitrary rooted networks

Abstract. We present a deterministic distributed depth-first token passing protocol on a rooted network. This protocol uses neither the processor identifiers nor 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. Our protocol implements a strictly fair token circulation scheme. The proposed protocol has extremely small state requirement – only $3(\Delta +1)$ states per processor, i.e., $O(log\;\Delta )$ bits per processor, where $\Delta$ is the degree of the network. The protocol can be used to implement a strictly fair distributed mutual exclusion in any rooted network. This protocol can also be used to construct a DFS spanning tree.