A self-stabilizing algorithm for constructing spanning trees

The term self-stabilizing was originally introduced by Dijkstra (1974) to distinguish any system having the property that starting at any, possibly illegitimate, state, the system is guaranteed to converge to a legitimate state in finite time, and, once in a legitimate state, it will remain so forever. Such a property is very desirable for any distributed system because, after any unexpected perturbation, the system eventually recovers and returns to a legitimate state without any outside intervention. A self-stabilizing algorithm is proposed for constructing spanning trees for connected graphs. Because of the self-stabilizing property, the algorithm can handle error recovery automatically.