The Time Complexity of Consensus Under Oblivious Message Adversaries

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Algorithmica Pub Date : 2024-02-13 DOI:10.1007/s00453-024-01209-4

Kyrill Winkler, Ami Paz, Hugo Rincon Galeana, Stefan Schmid, Ulrich Schmid

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Abstract

We study the problem of solving consensus in synchronous directed dynamic networks, in which communication is controlled by an oblivious message adversary that picks the communication graph to be used in a round from a fixed set of graphs \(\textbf{D}\) arbitrarily. In this fundamental model, determining consensus solvability and designing efficient consensus algorithms is surprisingly difficult. Enabled by a decision procedure that is derived from a well-established previous consensus solvability characterization for a given set \(\textbf{D}\), we study, for the first time, the time complexity of solving consensus in this model: We provide both upper and lower bounds for this time complexity, and also relate it to the number of iterations required by the decision procedure. Among other results, we find that reaching consensus under an oblivious message adversary can take exponentially longer than both deciding consensus solvability and broadcasting the input value of some unknown process to all other processes.

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忽略信息对手情况下达成共识的时间复杂性

我们研究的是同步有向动态网络中的共识求解问题，在这种网络中，通信是由一个遗忘信息对抗者控制的，对抗者会从一组固定的图（\textbf{D}\）中任意挑选一轮中要使用的通信图。在这个基本模型中，确定共识可解性和设计高效共识算法的难度之大令人吃惊。我们从之前针对给定集合 \(\textbf{D}\)建立的共识可解性表征中推导出了一个决策程序，在这个决策程序的帮助下，我们首次研究了在这个模型中求解共识的时间复杂度：我们提供了时间复杂度的上限和下限，并将其与决策程序所需的迭代次数联系起来。除其他结果外，我们还发现，与决定共识可解性和向所有其他进程广播某些未知进程的输入值相比，在遗忘信息对抗下达成共识所需的时间可能会呈指数级增长。

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来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.

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