Reaching Approximate Byzantine Consensus with Multi-hop Communication

  • Lili SuEmail author
  • Nitin Vaidya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9212)


We address the problem of reaching approximate consensus in the presence of Byzantine faults in a synchronous system. We analyze iterative algorithms that maintain minimal state, and impose the constraint that in each iteration the nodes may only communicate with other nodes that are up to l hops away. For a given l, we prove a necessary and sufficient condition on the network structure for the existence of correct iterative algorithms that achieve approximate Byzantine consensus. We prove sufficiency of the condition by designing a correct algorithm, which uses a trim function based on a minimal messages cover property introduced in this paper. Our necessary and sufficient condition generalizes the tight condition identified in prior work for \(l=1\). For \(l\ge l^*\), where \(l^*\) is the length of a longest cycle-free path in the given network, our condition is equivalent to the necessary and sufficient conditions for exact consensus in undirected and directed networks both.


Approximate byzantine consensus Iterative algorithm Synchronous system Incomplete network Bounded length communication paths 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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