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 $d$, for an appropriate definition of degeneracy. Recently at IWOCA 2019, Conte, Kant\'e, Marino, and Uno asked whether, even for a more restrictive notion of degeneracy, this XP-delay algorithm parameterized by $d$ could be made FPT-delay parameterized by $d$ and the maximum degree $\Delta$, i.e., an algorithm with delay $f(d,\Delta)\cdot n^{O(1)}$ for some computable function $f$. We answer this question in the affirmative whenever the hypergraph corresponds to the closed neighborhoods of a graph, i.e., we show that the intimately related problem of enumerating minimal dominating sets in graphs admits an FPT-delay algorithm parameterized by the degeneracy and the maximum degree.

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，该技术可针对退化度$d$的$n$顶点超图（采用适当的退化度定义），以$n^{O(d)}$延迟的算法枚举其所有极小横贯。近期在2019年IWOCA会议上，Conte、Kanté、Marino和Uno提出疑问：即使在更严格的退化度定义下，这种以$d$为参数的XP延迟算法能否改进为以$d$和最大度$\Delta$为参数的FPT延迟算法，即存在可计算函数$f$使得算法延迟为$f(d,\Delta)\cdot n^{O(1)}$。当超图对应于图的闭邻域时，我们对此问题给出肯定回答，具体而言，我们证明了图中密切相关的最小支配集枚举问题存在以退化度和最大度为参数的FPT延迟算法。