Optimal approximate-agreement error for at least three processes

Determine the optimal error probability for approximate agreement in the stochastic broadcast model with n≥3 processes, including the one-round case.

Background

The paper contrasts consensus with approximate agreement in the stochastic broadcast model. For two processes, prior work showed a close relationship between the optimal error probabilities of the two tasks, but for three processes approximate agreement may require fractional outputs and is no longer equivalent to binary consensus.

Although approximate agreement has therefore been studied in this setting, the authors state that its optimal error probability has not been determined for any number of processes n≥3, even when algorithms are restricted to one communication round.