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.
@article{arxiv.1805.02401,
title = {Acyclic Strategy for Silent Self-Stabilization in Spanning Forests},
author = {Karine Altisen and Stéphane Devismes and Anaïs Durand},
journal= {arXiv preprint arXiv:1805.02401},
year = {2018}
}