We presents a self-stabilizing algorithm for the unison problem which achieves an efficient trade-off between time, workload and space in a weak model. Our algorithm is defined in the atomic-state model and works in a simplified version of the \emph{stone age} model in which networks are anonymous and local ports are unlabelled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon. Assuming a period $B \geq 2D+2$, our algorithm stabilizes in at most $2D-2$ rounds and $O(\min(n^2B, n^3))$ moves, while using $\lceil\log B\rceil +2$ bits per node where $D$ is the network diameter and $n$ the number of nodes. In particular and to the best of our knowledge, it is the first self-stabilizing unison for arbitrary anonymous networks achieving an asymptotically optimal stabilization time in rounds using a bounded memory at each node. Finally, we show that our solution allows to efficiently simulate synchronous self-stabilizing algorithms in an asynchronous environment. This provides new state-of-the-art algorithm solving both the leader election and the spanning tree construction problem in any identified connected network which, to the best of our knowledge, beat all known solutions in the literature.

翻译：本文提出了一种针对一致问题的自稳定算法，该算法在弱模型中实现了时间、工作负载和空间之间的高效权衡。我们的算法基于原子状态模型，并在简化版“石器时代”模型中运行，其中网络是匿名的且本地端口未标记。算法不对守护进程做任何假设，因此能在最弱的分布式不公平守护进程下稳定。假设周期$B \geq 2D+2$，该算法最多在$2D-2$轮内稳定，移动次数为$O(\min(n^2B, n^3))$，每节点使用$\lceil\log B\rceil +2$比特内存，其中$D$是网络直径，$n$是节点数。特别地，据我们所知，这是首个针对任意匿名网络、在每节点使用有界内存且实现渐近最优轮数稳定时间的自稳定一致算法。最后，我们证明该解决方案能高效地在异步环境中模拟同步自稳定算法。这为任意标识连通网络中的领导者选举和生成树构建问题提供了新的一流算法，据我们所知，其性能优于文献中所有已知解决方案。