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Asymptotic Subspace Consensus in Dynamic Networks

Authors Matthias Függer , Thomas Nowak

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • Averaging
  • dynamic networks
  • consensus
  • higher dimensional

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Abstract

We introduce the problem of asymptotic subspace consensus, which requires the outputs of processes to converge onto a common subspace while remaining inside the convex hull of initial vectors. This is a relaxation of asymptotic consensus in which outputs have to converge to a single point, i.e., a zero-dimensional affine subspace.
We give a complete characterization of the solvability of asymptotic subspace consensus in oblivious message adversaries. In particular, we show that a large class of algorithms used for asymptotic consensus gracefully degrades to asymptotic subspace consensus in distributed systems with weaker assumptions on the communication network. We also present bounds on the rate by which a lower-than-initial dimension is reached.

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Matthias Függer and Thomas Nowak. Asymptotic Subspace Consensus in Dynamic Networks. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SAND.2026.10

Author Details

Matthias Függer
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France
Thomas Nowak
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France
  • Institut Universitaire de France, Paris, France

Funding

The work was supported by the French National Research Agency (ANR) projects DREAMY (ANR-21-CE48-0003) and COSTXPRESS (ANR-23-CE45-0013), as well as the SAIF project, funded by the "France 2030" government investment plan managed by ANR, under the reference ANR-23-PEIA-0006.

Acknowledgements

We thank Emmanuel Godard and Eloi Perdereau for introducing us to the question of possible generalizations of the asymptotic consensus problem.

Supplementary Materials

References

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