The first generic self-stabilizing transformer for local problems in a constrained bandwidth model is introduced. This transformer can be applied to a wide class of locally checkable labeling (LCL) problems, converting a given fault free synchronous algorithm that satisfies certain conditions into a self-stabilizing synchronous algorithm for the same problem. The resulting self-stabilizing algorithms are anonymous, size-uniform, and \emph{fully adaptive} in the sense that their time complexity is bounded as a function of the number $k$ of nodes that suffered faults (possibly at different times) since the last legal configuration. Specifically, for graphs whose degrees are up-bounded by $\Delta$, the algorithms produced by the transformer stabilize in time proportional to $\log (k + \Delta)$ in expectation, independently of the number of nodes in the graph. As such, the transformer is applicable also for infinite graphs (with degree bound $\Delta$). Another appealing feature of the transformer is its small message size overhead. The transformer is applied to known algorithms (or simple variants thereof) for some classic LCL problems, producing the first anonymous size-uniform self-stabilizing algorithms for these problems that are provably fully adaptive. From a technical point of view, the transformer's key design feature is a novel probabilistic tool that allows different nodes to act in synchrony even though their clocks may have been adversarially manipulated.

翻译：本文首次在受限带宽模型中引入了针对局部问题的通用自稳定转换器。该转换器可应用于广泛的局部可检查标记（LCL）问题类别，将满足特定条件的无故障同步算法转换为针对同一问题的自稳定同步算法。所得的自稳定算法具有匿名性、规模一致性，且具备完全自适应性——其时间复杂度受限于自上次合法配置以来发生故障（可能在不同时间）的节点数$k$的函数。具体而言，对于度数上限为$\Delta$的图，该转换器生成的算法在期望时间内以与$\log (k + \Delta)$成正比的速度稳定，且与图中节点总数无关。因此，该转换器也适用于具有度数限制$\Delta$的无限图。该转换器的另一突出特性是其较小的消息尺寸开销。通过将该转换器应用于若干经典LCL问题的已知算法（或其简单变体），首次为这些问题提供了可证明完全自适应的匿名规模一致自稳定算法。从技术角度看，该转换器的核心设计特征是新颖的概率工具，即使各节点的时钟被对抗性操纵，该工具仍能保证不同节点实现同步操作。