Asynchronous Approximate Agreement with Quadratic Communication

We consider an asynchronous network of $n$ message-sending parties, up to $t$ of which are byzantine. We study approximate agreement, where the parties obtain approximately equal outputs in the convex hull of their inputs. In their seminal work, Abraham, Amit and Dolev [OPODIS '04] achieve this with the optimal resilience $t < \frac{n}{3}$ with a protocol where each party reliably broadcasts its input every iteration. This takes $\Theta(n^2)$ messages per reliable broadcast, or $\Theta(n^3)$ messages per iteration.

@article{erbes2025_2408.05495,
  title={ Asynchronous Approximate Agreement with Quadratic Communication },
  author={ Mose Mizrahi Erbes and Roger Wattenhofer },
  journal={arXiv preprint arXiv:2408.05495},
  year={ 2025 }
}