In this article, we study the parameterized complexity of the Set Cover problem restricted to d-semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete \& Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in d-semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, that proves the tightness of our kernelization under standard complexity-theoretic assumptions.

翻译：本文研究了限制在d-半梯形自由超图上的集合覆盖问题的参数化复杂度，该类超图由Fabianski等人定义[参见STACS 2019会议论文集]。我们观察到Langerman与Morin[参见《离散与计算几何》2005年]在几何覆盖问题中引入的两个算法可适用于该场景，从而为d-半梯形自由超图上的集合覆盖问题提供了简洁的FPT（固定参数可解）算法与核化算法。在算法结论之外，我们还给出了该问题的压缩下界，在标准复杂度理论假设下证明了核化算法的紧致性。