We propose a way to transform synchronous distributed algorithms solving locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks. Mendable problems are a generalization of greedy problems where any partial solution may be transformed -- instead of completed -- into a global solution: every time we extend the partial solution we are allowed to change the previous partial solution up to a given distance. Locally here means that to extend a solution for a node, we need to look at a constant distance from it. In order to do this, we propose the first explicit self-stabilizing algorithm computing a $(k,k-1)$-ruling set (i.e. a "maximal independent set at distance $k$"). By combining multiple time this technique, we compute a distance-$K$ coloring of the graph. With this coloring we can finally simulate \local~model algorithms running in a constant number of rounds, using the colors as unique identifiers. Our algorithms work under the Gouda daemon, which is similar to the probabilistic daemon: if an event should eventually happen, it will occur under this daemon.

翻译：我们提出一种方法，将求解局部贪心且可修补问题的同步分布式算法转化为匿名网络中的自稳定算法。可修补问题是贪心问题的推广，其中任意部分解可被转化（而非补全）为全局解：每次扩展部分解时，允许对先前部分解进行给定距离内的修改。此处“局部”指对某个节点扩展解时，仅需考察其常数距离内的信息。为此，我们首次提出显式自稳定算法来计算$(k,k-1)$-统治集（即“距离$k$上的极大独立集”）。通过多次组合该技术，我们可计算图的距离-$K$着色。利用此着色，我们最终能以颜色作为唯一标识符，模拟在常数轮内运行的\local~模型算法。我们的算法在Gouda守护进程下工作——该守护进程类似于概率守护进程：若某事件终将发生，则在此守护进程下必然发生。