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Reports (Research Report) Year : 2013

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. Important disclaimer: these results have NOT yet been published in an international conference or journal. This is just a technical report presenting intermediary and incomplete results. A generalized version of these results may be under submission.
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Dates and versions

hal-00773343 , version 1 (13-01-2013)
hal-00773343 , version 2 (22-01-2013)
hal-00773343 , version 3 (09-02-2013)
hal-00773343 , version 4 (07-12-2013)

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Cite

Alexandre Maurer, Sébastien Tixeuil. On Byzantine Broadcast in Planar Graphs. [Research Report] _. 2013. ⟨hal-00773343v4⟩
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