We present the $\delta$-Synchronizer, which works in non-synchronous dynamic networks under minimal assumptions. Our model allows for arbitrary topological changes without any guarantee of eventual global or partial stabilization and assumes that nodes are anonymous. This deterministic synchronizer is the first that enables nodes to simulate a dynamic network synchronous algorithm for executions in a semi-synchronous dynamic environment under a weakly-fair node activation scheduler, despite the absence of a global clock, node ids, persistent connectivity or any assumptions about the edge dynamics (in both the synchronous and semi-synchronous environments). We make the following contributions: (1) we extend the definition of synchronizers to networks with arbitrary edge dynamics; (2) we present the first synchronizer from the semi-synchronous to the synchronous model in such networks; and (3) we present non-trivial applications of the proposed synchronizer to existing algorithms. We assume an extension of the Pull communication model by adding a single 1-bit multi-writer atomic register at each edge-port of a node. We show that this extension is needed and that synchronization in our setting is not possible without it. The $\delta$-Synchronizer operates with a multiplicative memory overhead at the nodes that is asymptotically logarithmic on the runtime of the underlying synchronous algorithm being simulated-in particular, it is logarithmic for polynomial-time synchronous algorithms.

翻译：我们提出了一种在最小假设条件下适用于非同步动态网络的$\delta$-同步器。该模型允许任意拓扑变化，无需保证最终全局或局部稳定性，并假设节点为匿名状态。这一确定性同步器首次使得节点能够在弱公平节点激活调度器的半同步动态环境中，模拟动态网络同步算法的执行过程，尽管缺乏全局时钟、节点标识符、持久连通性或任何关于边动态的假设（在同步与半同步环境中均适用）。我们的贡献包括：（1）将同步器的定义扩展至具有任意边动态的网络；（2）在此类网络中首次提出从半同步模型到同步模型的同步器；（3）将所提同步器应用于现有算法并展示其非平凡应用价值。我们假设对Pull通信模型进行了扩展，在节点的每个边端口处添加一个单比特多写入原子寄存器。我们证明该扩展是必要的，且在此设定下若无此扩展则无法实现同步。$\delta$-同步器在节点处产生的乘法内存开销，相对于被模拟的底层同步算法运行时间呈渐近对数级增长——特别地，对于多项式时间复杂度的同步算法，其开销为对数级。