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Exact Byzantine Consensus on Arbitrary Directed Graphs Under Local Broadcast Model

Authors Muhammad Samir Khan, Lewis Tseng, Nitin H. Vaidya

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Author Details

Muhammad Samir Khan
  • Department of Computer Science, University of Illinois at Urbana-Champaign, USA
Lewis Tseng
  • Department of Computer Science, Boston College, USA
Nitin H. Vaidya
  • Department of Computer Science, Georgetown University, USA

Funding

This research is supported in part by the National Science Foundation awards 1409416 and 1733872, and Toyota InfoTechnology Center. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.

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Muhammad Samir Khan, Lewis Tseng, and Nitin H. Vaidya. Exact Byzantine Consensus on Arbitrary Directed Graphs Under Local Broadcast Model. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.OPODIS.2019.30

Abstract

We consider Byzantine consensus in a synchronous system where nodes are connected by a network modeled as a directed graph, i.e., communication links between neighboring nodes are not necessarily bi-directional. The directed graph model is motivated by wireless networks wherein asymmetric communication links can occur. In the classical point-to-point communication model, a message sent on a communication link is private between the two nodes on the link. This allows a Byzantine faulty node to equivocate, i.e., send inconsistent information to its neighbors. This paper considers the local broadcast model of communication, wherein transmission by a node is received identically by all of its outgoing neighbors, effectively depriving the faulty nodes of the ability to equivocate.
Prior work has obtained sufficient and necessary conditions on undirected graphs to be able to achieve Byzantine consensus under the local broadcast model. In this paper, we obtain tight conditions on directed graphs to be able to achieve Byzantine consensus with binary inputs under the local broadcast model. The results obtained in the paper provide insights into the trade-off between directionality of communication links and the ability to achieve consensus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • complexity and impossibility results for distributed computing
  • fault-tolerance
  • reliability

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