  In this paper, we formalize design patterns, commonly used in the
self-stabilizing area, to obtain general statements regarding both correctness
and time complexity guarantees. Precisely, we study a general class of
algorithms designed for networks endowed with a sense of direction describing a
spanning forest (e.g., a directed tree or a network where a directed spanning
tree is available) whose characterization is a simple (i.e., quasi-syntactic)
condition. We show that any algorithm of this class is (1) silent and
self-stabilizing under the distributed unfair daemon, and (2) has a
stabilization time which is polynomial in moves and asymptotically optimal in
rounds. To illustrate the versatility of our method, we review several existing
works where our results apply.
