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arXiv 1311.6902cs.DC
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好,更好,最好!- 不可战胜的共识和共识集协议

Good, Better, Best! - Unbeatable Protocols for Consensus and Set Consensus

Armando Castañeda, Yannai A. Gonczarowski, Yoram Moses

摘要:

虽然同步模型的第一个共识协议被设计为匹配最坏情况下的下限,在所有运行中精确地在t+1轮中决定,但很快就意识到它们可以通过早期停止协议进行严格改进。它们在第一轮中占主导地位,总是在最多t+1轮中决定,但通常要快得多。一个协议如果不能被严格控制,那么它就是不可战胜的。对于分布式协议来说,不可击败性通常是比最坏情况性能更合适的最优性概念。利用基于知识的分析方法,研究了一致性和k-集一致性的不可战胜性。我们提出了无与伦比的解决方案,以非统一的共识和k集共识,并在同步消息传递上下文中的统一共识崩溃失败。k-集一致性问题比一致性问题在技术上更具挑战性,它的分析引发了分布式计算拓扑方法的发展。这个问题的最坏情况下的下限需要基于代数拓扑的技术,或基于简化的证明。我们对不可战胜性的证明纯粹是组合的,是对共识性的直接推广,尽管不是微不足道的。我们还提出了一种替代拓扑不可战胜的证明,可以理解的连接协议复杂的过程和决策时间之间的连接。对于同步模型,仅提供了k集共识的统一变体的解决方案。基于我们无与伦比的协议一致的共识和非一致的k-集共识,我们提出了一个一致的k-集共识协议,严格主导所有已知的解决方案,这个问题的同步模型。

英文摘要:

While the very first consensus protocols for the synchronous model were designed to match the worst-case lower bound, deciding in exactly t+1 rounds in all runs, it was soon realized that they could be strictly improved upon by early stopping protocols. These dominate the first ones, by always deciding in at most t+1 rounds, but often much faster. A protocol is unbeatable if it can't be strictly dominated. Unbeatability is often a much more suitable notion of optimality for distributed protocols than worst-case performance. Using a knowledge-based analysis, this paper studies unbeatability for both consensus and k-set consensus. We present unbeatable solutions to non-uniform consensus and k-set consensus, and uniform consensus in synchronous message-passing contexts with crash failures. The k-set consensus problem is much more technically challenging than consensus, and its analysis has triggered the development of the topological approach to distributed computing. Worst-case lower bounds for this problem have required either techniques based on algebraic topology, or reduction-based proofs. Our proof of unbeatability is purely combinatorial, and is a direct, albeit nontrivial, generalization of the one for consensus. We also present an alternative topological unbeatability proof that allows to understand the connection between the connectivity of protocol complexes and the decision time of processes. For the synchronous model, only solutions to the uniform variant of k-set consensus have been offered. Based on our unbeatable protocols for uniform consensus and for non-uniform k-set consensus, we present a uniform k-set consensus protocol that strictly dominates all known solutions to this problem in the synchronous model.

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