On Byzantine Broadcast in Planar Graphs

Abstract : We consider the problem of reliably broadcasting information in a multihop asynchronous network in the presence of Byzantine failures: some nodes may exhibit unpredictable malicious behavior. We focus on completely decentralized solutions. Few Byzantine-robust algorithms exist for loosely connected networks. A recent solution guarantees reliable broadcast on a torus when D > 4, D being the minimal distance between two Byzantine nodes. In this paper, we generalize this result to 4-connected planar graphs. We show that reliable broadcast can be guaranteed when D > Z, Z being the maximal number of edges per polygon. We also show that this bound on D is a lower bound for this class of graphs. Our solution has the same time complexity as a simple broadcast. This is also the first solution where the memory required increases linearly (instead of exponentially) with the size of transmitted information.
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https://hal.sorbonne-universite.fr/hal-00773343
Contributor : Alexandre Maurer <>
Submitted on : Saturday, February 9, 2013 - 2:52:39 AM
Last modification on : Thursday, October 17, 2019 - 12:36:04 PM
Long-term archiving on : Saturday, April 1, 2017 - 8:52:54 PM

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  • HAL Id : hal-00773343, version 3
  • ARXIV : 1301.2875

Citation

Alexandre Maurer, Sébastien Tixeuil. On Byzantine Broadcast in Planar Graphs. 2013. ⟨hal-00773343v3⟩

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