Optimal block-time distribution for minimizing fork rate

Determine the optimal block-time distribution that minimizes the fork rate subject to a fixed average block-time constraint in the PoVD mining model.

Background

The paper models PoVD using an arbitrary block-time distribution and derives closed-form expressions for both fork rate and average block time. These quantities represent a trade-off: reducing the average block time can improve throughput but may increase the probability that multiple blocks are generated during propagation, thereby increasing the fork rate.

The authors explicitly identify the optimization of the block-time distribution under a fixed block-time constraint as unresolved. They introduce a δ\delta-spaced distribution as a constructive, non-optimal distribution that can outperform PoW under specified network conditions, but they do not establish the globally optimal distribution.

References

Therefore, can we reduce the fork rate $\mathsf{F}\left(\tilde{p}\left(r\right)\right)$ with the same block time $\mathsf{B}\left(\tilde{p}\left(r\right)\right)$, by adjusting the distribution $\tilde{p}\left(r\right)$? Due to the complicated expressions of $\mathsf{F}\left(\tilde{p}\left(r\right)\right)$ and $\mathsf{B}\left(\tilde{p}\left(r\right)\right)$, this is a very challenging problem. So far, the optimal block time distribution to minimize the fork rate under the block time constraint remains open.

— PoVD: Efficient Consensus Protocol based on Verifiable Delay Function  (2609.21627 - Jiang et al., 18 Sep 2026) in Section "PoVD Block Time Re-Distribution," subsection "$\delta$-spaced Block Time Distribution"