A Near-Optimal Deterministic Distributed Synchronizer

TL;DR

This paper introduces a deterministic distributed synchronizer with near-optimal time and message complexities, enabling the first efficient asynchronous algorithms for fundamental tasks like leader election, BFS, and MST without randomness.

Contribution

It presents the first deterministic synchronizer with near-optimal overheads, fixing inaccuracies in prior randomized approaches, and applies it to achieve optimal asynchronous algorithms for key distributed problems.

Findings

Deterministic synchronizer with poly(log n) overheads

First asynchronous deterministic algorithms for leader election, BFS, MST

Optimal or near-optimal complexities up to logarithmic factors

Abstract

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.