We consider the problem of reliably broadcasting information in a multihop asynchronous network in the presence of Byzantine failures: some nodes have an unpredictable malicious behavior. We focus on totally decentralized solutions. Very few Byzantine-robust algorithms exist for loosely connected networks. A recent algorithm 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 is guaranteed when D > Z, Z being the maximal number of edges per polygon. We also show that this bound on D cannot be improved 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 with the size of informations, and not exponentially.
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