A Near-Optimal Deterministic Distributed Synchronizer
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We provide the first deterministic distributed synchronizer with near-optimal time complexity and message complexity overheads. Concretely, given any distributed algorithm ๐ 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 ๐' that runs in the asynchronous message-passing model with time complexity T ยท poly(log n) and message complexity (M+m)ยท 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 ๐ is deterministic, then so is algorithm ๐'. 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 ร(m) message complexity. The former two have ร(D) time complexity, where D denotes the network diameter, and the latter has ร(D+โ(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.
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