Gradual Stabilization Under \tau -Dynamics.

In this paper, we introduce the notion of gradually stabilizing algorithm as any self-stabilizing algorithm with the following additional feature: if at most $$\\tau $$dynamic steps occur starting from a legitimate configuration, it first quickly recovers to a configuration from which a minimum quality of service is satisfied and then gradually converges to stronger and stronger safety guarantees until reaching a legitimate configuration again. We illustrate this new property by proposing a gradually stabilizing unison algorithm.