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Communication cost of consensus for nodes with limited memory.

  • Fanti G Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213.
  • Holden N Institute for Theoretical Studies, Swiss Federal Institute of Technology (ETH) Zürich, 8092 Zürich, Switzerland.
  • Peres Y Microsoft Research, Redmond, WA 98052; yperes@gmail.com.
  • Ranade G Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720.
  • 2020-03-06
Published in:
  • Proceedings of the National Academy of Sciences of the United States of America. - 2020
communication
consensus
distributed computing
memory
Consensus
Information Storage and Retrieval
Internet of Things
Models, Theoretical
Wireless Technology
English 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., [Formula: see text] 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 [Formula: see text], consensus can be reached with linear communication cost, but this is impossible if [Formula: see text] 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.
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  • English
Open access status
bronze
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https://sonar.ch/global/documents/185197
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