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 maximum degree 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，该技术针对退化度为d的n顶点超图，给出了一个$n^{O(d)}$-延迟算法来枚举所有最小横贯。最近在2019年IWOCA会议上，Conte、Kanté、Marino和Uno提出疑问：这种以d为参数化的XP延迟算法是否可以在更弱的退化度概念下实现FPT延迟，甚至以最大度Δ为参数化？即是否存在可计算函数f，使得该算法能转化为延迟为$f(\Delta)\cdot n^{O(1)}$的算法。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也未能达到这些时间界。本文利用有序生成方法，证明可以设计出以最大度和维数为参数化的FPT延迟算法来枚举最小横贯，从而对该问题给出了更广义的肯定回答。