Enumeration problems are often encountered as key subroutines in the exact computation of graph parameters such as chromatic number, treewidth, or treedepth. In the case of treedepth computation, the enumeration of inclusion-wise minimal separators plays a crucial role. However and quite surprisingly, the complexity status of this problem has not been settled since it has been posed as an open direction by Kloks and Kratsch in 1998. Recently at the PACE 2020 competition dedicated to treedepth computation, solvers have been circumventing that by listing all minimal a-b separators and filtering out those that are not inclusion-wise minimal, at the cost of efficiency. Naturally, having an efficient algorithm for listing inclusion-wise minimal separators would drastically improve such practical algorithms. In this note, however, we show that no efficient algorithm is to be expected from an output-sensitive perspective, namely, we prove that there is no output-polynomial time algorithm for inclusion-wise minimal separators enumeration unless $\mathsf{P}=\mathsf{NP}$.

枚举问题是在精确计算图参数（例如色数、树宽或树深）时经常遇到的关键子例程。在树深度计算的情况下，包含明智的最小分隔符的枚举起着至关重要的作用。然而，令人惊讶的是，自从 Kloks 和 Kratsch 于 1998 年将其提出为开放方向以来，该问题的复杂性状况尚未得到解决。最近，在专注于树深度计算的 PACE 2020 竞赛中，求解器通过列出所有最小 a-b 分隔符并过滤掉那些不包含的分隔符 -明智的最小化，但以效率为代价。当然，拥有一个有效的算法来列出包含的最小分隔符将极大地改进这种实用算法。然而，在本文中，我们表明从输出敏感的角度来看，不存在有效的算法，即，我们证明不存在用于包含明智的最小分隔符枚举的输出多项式时间算法，除非 $\mathsf{磷}=\mathsf{NP}$。