On Byzantine Broadcast in Planar Graphs

TL;DR

This paper extends Byzantine broadcast solutions to 4-connected planar graphs, establishing a new reliability condition based on the maximum edges per polygon, with linear memory growth and efficient broadcast time.

Contribution

It generalizes previous results from torus networks to 4-connected planar graphs, providing a new reliability bound and a scalable memory solution.

Findings

Reliable broadcast guaranteed when D > Z, Z being max edges per polygon

Solution has same time complexity as simple broadcast

Memory increases linearly with transmitted information size

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.