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 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 $f$. Moreover, as a first step toward answering that question, they note that the same delay is open for the intimately related problem of listing all minimal dominating sets in graphs. In this paper, we answer the latter question in the affirmative.

翻译：在2002年的STOC会议上，Eiter、Gottlob和Makino提出了一种称为有序生成的技术，该技术能够以n^{O(d)}的延迟时间枚举n顶点、退化度为d的超图的所有最小横贯。近期在2019年的IWOCA会议上，Conte、Kanté、Marino和Uno提出疑问：这种以d为参数的XP-延迟算法能否改进为以d和最大度Δ为参数的FPT-延迟算法，即存在可计算函数f使得延迟时间为f(d,Δ)·n^{O(1)}的算法。此外，作为解答该问题的第一步，他们指出对于图论中密切相关的枚举所有最小支配集问题，相同的延迟时间仍是开放问题。本文中，我们对后一问题给出了肯定回答。