We provide the first deterministic distributed synchronizer with near-optimal time complexity and message complexity overheads. Concretely, given any distributed algorithm $\mathcal{A}$ that has time complexity $T$ and message complexity $M$ in the synchronous message-passing model (subject to some care in defining the model), the synchronizer provides a distributed algorithm $\mathcal{A}'$ that runs in the asynchronous message-passing model with time complexity $T \cdot poly(\log n)$ and message complexity $(M+m)\cdot poly(\log n)$. Here, $n$ and $m$ denote the number of nodes and edges in the network, respectively. The synchronizer is deterministic in the sense that if algorithm $\mathcal{A}$ is deterministic, then so is algorithm $\mathcal{A}'$. Previously, only a randomized synchronizer with near-optimal overheads was known by seminal results of Awerbuch, Patt-Shamir, Peleg, and Saks [STOC 1992] and Awerbuch and Peleg [FOCS 1990]. We also point out and fix some inaccuracies in these prior works. As concrete applications of our synchronizer, we resolve some longstanding and fundamental open problems in distributed algorithms: we get the first asynchronous deterministic distributed algorithms with near-optimal time and message complexities for leader election, breadth-first search tree, and minimum spanning tree computations: these all have message complexity $\tilde{O}(m)$ message complexity. The former two have $\tilde{O}(D)$ time complexity, where $D$ denotes the network diameter, and the latter has $\tilde{O}(D+\sqrt{n})$ time complexity. All these bounds are optimal up to logarithmic factors. Previously all such near-optimal algorithms were either restricted to the synchronous setting or required randomization.

翻译：我们提供了首个具有近优时间复杂度和消息复杂度开销的确定性分布式同步器。具体而言，给定任意在同步消息传递模型下具有时间复杂度$T$和消息复杂度$M$的分布式算法$\mathcal{A}$（需对模型定义进行适当调整），该同步器可构造一个在异步消息传递模型下运行的分布式算法$\mathcal{A}'$，其时间复杂度为$T \cdot poly(\log n)$，消息复杂度为$(M+m)\cdot poly(\log n)$。其中$n$和$m$分别表示网络中的节点数和边数。该同步器是确定性的，即若算法$\mathcal{A}$是确定性的，则算法$\mathcal{A}'$也是确定性的。此前，仅由Awerbuch、Patt-Shamir、Peleg和Saks [STOC 1992]以及Awerbuch和Peleg [FOCS 1990]的开创性工作给出了具有近优开销的随机化同步器。我们还指出并修正了这些先前工作中存在的一些不精确之处。作为我们同步器的具体应用，我们解决了分布式算法中一些长期存在的根本性开放问题：首次实现了领导者选举、广度优先搜索树和最小生成树计算的异步确定性分布式算法，且具有近优时间复杂度和消息复杂度：这些算法的消息复杂度均为$\tilde{O}(m)$，前两个算法的时间复杂度为$\tilde{O}(D)$（$D$表示网络直径），最后一个算法的时间复杂度为$\tilde{O}(D+\sqrt{n})$。所有这些界在对数因子意义下均为最优。此前，所有这类近优算法要么局限于同步环境，要么需要随机化。