A vertex subset $S \subseteq V$ is an $(a,b)$ separator for nonadjacent vertices $a$ and $b$ if the removal of $S$ from a graph $G$ separates $a$ and $b$ into distinct connected components.
$S$ is a minimal $(a,b)$ separator if no proper subset of $S$ separates $a$ and $b$.
It is known [1] that all minimal $(a,b)$ separators in an undirected connected graph can be computed in $O(n^2 R_{ab})$ time, where $R_{ab}$ is the number of minimal $(a,b)$ separators.
Question 1. Are there any results showing that this enumeration can be done more efficiently when restricted to DAGs?
Question 2. Is there a simpler algorithm than [1] to do the enumeration in a DAG?
[1] Shen, Hong, Keqin Li, and Si-Qing Zheng. "Separators are as simple as cutsets." Annual Asian Computing Science Conference. Springer, Berlin, Heidelberg, 1999.