The Self-Stabilizing Edge-Token and Its Applications

Consider a connected graph with nodes (or processes) and edges (or communication links). An edge token associated with an edge is a token maintained by the two nodes connected by the edge; one and only one of the two nodes holds the token. An edge to- ken can be passed from one node to the other if so desired. This paper first presents a randomized self-stabilizing algorithm to implement the edge token, in which each proc- ess maintains two three-state variables for an edge; the scheme works under the distrib- uted scheduler with the read/write atomicity. Then, the edge token algorithm is used as a building block in two other self-stabilizing algorithms: one is for ring orientation prob- lem and the other for token circulation problem on trees. All the proposed algorithms are uniform.

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