We present a self-stabilizing algorithm for the (asynchronous) unison problem which achieves an efficient trade-off between time, workload, and space in a weak model. Precisely, our algorithm is defined in the atomic-state model and works in anonymous networks in which even local ports are unlabeled. It makes no assumption on the daemon and thus stabilizes under the weakest one: the distributed unfair daemon. In a $n$-node network of diameter $D$ and assuming a period $B \geq 2D+2$, our algorithm only requires $O(\log B)$ bits per node to achieve full polynomiality as it stabilizes in at most $2D-2$ rounds and $O(\min(n^2B, n^3))$ moves. 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 a 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 existing solutions of the literature.

翻译：我们提出了一种针对（异步）Unison问题的自稳定算法，该算法在弱模型下实现了时间、工作负载与空间的高效权衡。具体而言，我们的算法在原子状态模型中定义，适用于连局部端口都未标记的匿名网络。该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。在直径为$D$的$n$节点网络中，假设周期$B \geq 2D+2$，算法仅需每个节点$O(\log B)$比特即可实现完全多项式特性：至多经过$2D-2$轮和$O(\min(n^2B, n^3))$次移动即可稳定。特别值得注意的是，据我们所知，这是首个针对任意匿名网络、在每节点有限内存下实现渐进最优稳定轮数的自稳定Unison算法。最后，我们证明该算法能在异步环境中高效模拟同步自稳定算法。由此得到的最先进算法可解决任意连通标识网络中的领导者选举和生成树构建问题，据我们所知，该算法超越了文献中所有现有方案。