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

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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)


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
  • dynamic networks
  • oblivious message adversaries
  • consensus
  • time complexity


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