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Computing Outside the Box: Average Consensus over Dynamic Networks

Authors Bernadette Charron-Bost, Patrick Lambein-Monette

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Author Details

Bernadette Charron-Bost
  • Département d'informatique de l'ENS, ENS, CNRS, PSL University, Paris, France
Patrick Lambein-Monette
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France

Acknowledgements

Patrick Lambein-Monette would like to thank his doctoral jury for stimulating discussions and remarks regarding previous versions of this material.

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Bernadette Charron-Bost and Patrick Lambein-Monette. Computing Outside the Box: Average Consensus over Dynamic Networks. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SAND.2022.10

Abstract

Networked systems of autonomous agents, and applications thereof, often rely on the control primitive of average consensus, where the agents are to compute the average of private initial values. To provide reliable services that are easy to deploy, average consensus should continue to operate when the network is subject to frequent and unpredictable change, and should mobilize few computational resources, so that deterministic, low powered, and anonymous agents can partake in the network. In this stringent adversarial context, we investigate the implementation of average consensus by distributed algorithms over networks with bidirectional, but potentially short-lived, communication links. Inspired by convex recurrence rules for multi-agent systems, and the Metropolis average consensus rule in particular, we design a deterministic distributed algorithm that achieves asymptotic average consensus, which we show to operate in polynomial time in a synchronous temporal model. The algorithm is easy to implement, has low space and computational complexity, and is fully distributed, requiring neither symmetry-breaking devices like unique identifiers, nor global control or knowledge of the network. In the fully decentralized model that we adopt, to our knowledge, no other distributed average consensus algorithm has a better temporal complexity. Our approach distinguishes itself from classical convex recurrence rules in that the agent’s values may sometimes leave their previous convex hull. As a consequence, our convergence bound requires a subtle analysis, despite the syntactic simplicity of our algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Computing methodologies → Distributed artificial intelligence
  • Networks → Sensor networks
  • Networks → Mobile networks
  • Networks → Network dynamics
Keywords
  • average consensus
  • dynamic networks
  • distributed algorithms
  • iterated averaging
  • Metropolis

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