文章基本信息

标题：Communication cost of consensus for nodes with limited memory
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作者：Giulia Fanti ; Nina Holden ; Yuval Peres 等
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2020
卷号：117
期号：11
页码：5624-5630
DOI：10.1073/pnas.1912980117
出版社：The National Academy of Sciences of the United States of America
摘要：Motivated by applications in wireless networks and the Internet of Things, we consider a model of n nodes trying to reach consensus with high probability on their majority bit. Each node i is assigned a bit at time 0 and is a finite automaton with m bits of memory (i.e., 2 m states) and a Poisson clock. When the clock of i rings, i can choose to communicate and is then matched to a uniformly chosen node j. The nodes j and i may update their states based on the state of the other node. Previous work has focused on minimizing the time to consensus and the probability of error, while our goal is minimizing the number of communications. We show that, when m > 3 ⁡ log ⁡ log ⁡ log ( n ) , consensus can be reached with linear communication cost, but this is impossible if m < log ⁡ log ⁡ log ( n ) . A key step is to distinguish when nodes can become aware of knowing the majority bit and stop communicating. We show that this is impossible if their memory is too low.
关键词：distributed computing ; consensus ; communication ; memory