At STOC 2002, Eiter, Gottlob, and Makino presented a technique called ordered generation that yields an $n^{O(d)}$-delay algorithm listing all minimal transversals of an $n$-vertex hypergraph of degeneracy $d$. Recently at IWOCA 2019, Conte, Kant\'e, Marino, and Uno asked whether this XP-delay algorithm parameterized by $d$ could be made FPT-delay for a weaker notion of degeneracy, or even parameterized by the maximum degree $\Delta$, i.e., whether it can be turned into an algorithm with delay $f(\Delta)\cdot n^{O(1)}$ for some computable function $f$. Moreover, and as a first step toward answering that question, they note that they could not achieve these time bounds even for the particular case of minimal dominating sets enumeration. In this paper, using ordered generation, we show that an FPT-delay algorithm can be devised for minimal transversals enumeration parameterized by the degeneracy and dimension, giving a positive and more general answer to the latter question.

翻译：在 2002 年 STOC 会议上，Eiter、Gottlob 和 Makino 提出了一种称为有序生成的技术，该技术可生成一个 $n^{O(d)}$-延迟算法，用于枚举具有退化度 $d$ 的 $n$ 顶点超图的所有最小横贯。近期在 2019 年 IWOCA 会议上，Conte、Kanté、Marino 和 Uno 提出疑问：这种以 $d$ 为参数的 XP-延迟算法能否对于退化度的较弱概念变为 FPT-延迟，甚至以最大度 $\Delta$ 为参数（即能否将其转化为一个延迟为 $f(\Delta)\cdot n^{O(1)}$ 的算法，其中 $f$ 为某个可计算函数）。此外，作为回答该问题的第一步，他们指出即使在最小支配集枚举这一特例中，他们也未能达到这些时间界限。在本文中，利用有序生成，我们证明可以设计出一种以退化度和维数为参数的 FPT-延迟算法用于枚举最小横贯，从而对该后一个问题给出了肯定且更一般的回答。