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The Time Complexity of Consensus Under Oblivious Message Adversaries

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

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Author Details

Kyrill Winkler
  • ITK Engineering, Wien, Austria
Ami Paz
  • LISN - CNRS & Paris-Saclay University, France
Hugo Rincon Galeana
  • TU Wien, Austria
Stefan Schmid
  • TU Berlin, Germany
  • Fraunhofer SIT, Darmstadt, Germany
Ulrich Schmid
  • TU Wien, Austria

Funding

This research has received funding from the German Federal Ministry of Education and Research (BMBF), 6G-RIC, grant 16KISK020K; Vienna Science and Technology Fund (WWTF) project ICT19-045; Austrian Science Fund (FWF) projects ADynNet P28182, ByzDEL P33600, and netIDEE SCIENCE P33775-N.
  • Winkler, Kyrill: Vienna Science and Technology Fund (WWTF) project ICT19-045, 2020-2024.
  • Rincon Galeana, Hugo: Supported by the Doctoral College on Resilient Embedded Systems at TU Wien.

Cite AsGet BibTex

Kyrill Winkler, Ami Paz, Hugo Rincon Galeana, Stefan Schmid, and Ulrich Schmid. The Time Complexity of Consensus Under Oblivious Message Adversaries. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 100:1-100:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITCS.2023.100

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 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 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Networks
Keywords
  • dynamic networks
  • oblivious message adversaries
  • consensus
  • time complexity

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