Hypergraph Dualization with FPT-delay Parameterized by the Degeneracy and Dimension
Abstract: 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, Kanté, Marino, and Uno asked whether this \(\textsf{XP}\)-delay algorithm parameterized by d could be made \(\textsf{FPT}\)-delay for a weaker notion of degeneracy, or even parameterized by the maximum degree \(\varDelta \), i.e., whether it can be turned into an algorithm with delay \(f(\varDelta )\cdot n^{O(1)}\) 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 \(\textsf{FPT}\)-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.
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