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Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement
"... Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. ..."
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Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of faulttolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. The complexity of set agreement in synchronous networks has also been a significant research challenge. Real systems, however, are neither purely synchronous nor purely asynchronous. Rather, they tend to alternate between periods of synchrony and periods of asynchrony. In this paper, we analyze the complexity of set agreement in a such a “partially synchronous ” setting, presenting the first (asymptotically) tight bound on the complexity of set agreement in such systems. We introduce a novel technique for simulating, in faultprone asynchronous shared memory, executions of an asynchronous and failureprone messagepassing system in which some fragments appear synchronous to some processes. We use this technique to derive a lower bound on the round complexity of set agreement in a partially synchronous system by a reduction from asynchronous waitfree set agreement. We also present an asymptotically matching algorithm that relies on a distributed asynchrony detection mechanism to decide as soon as possible during periods of synchrony. By relating environments with differing degrees of synchrony, our simulation technique is of independent interest. In particular, it allows us to obtain a new lower bound on the complexity of early deciding kset agreement complementary to that of [12], and to rederive the combinatorial topology lower bound of [13] in an algorithmic way. 1
Brief Announcement: Pareto Optimal Solutions to Consensus and Set Consensus
"... A protocol P is Paretooptimal if no protocolQ can decide as fast as P for all adversaries, while allowing at least one process to decide strictly earlier, in at least one instance. Pareto optimal protocols cannot be improved upon. We present the first Paretooptimal solutions to consensus and kse ..."
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A protocol P is Paretooptimal if no protocolQ can decide as fast as P for all adversaries, while allowing at least one process to decide strictly earlier, in at least one instance. Pareto optimal protocols cannot be improved upon. We present the first Paretooptimal solutions to consensus and kset consensus for synchronous messagepassing with crashes failures. Our kset consensus protocol strictly dominates all known solutions, and our results expose errors in [1, 7, 8, 12]. Our proofs of Pareto optimality are completely constructive, and are devoid of any topological arguments or reductions. Categories and Subject Descriptors