In this article, we study the parameterized complexity of the Set Cover problem restricted to 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 semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

翻译：本文研究了限制在半梯无超图（由Fabianski等人在STACS 2019会议论文中定义的一类超图）上的集合覆盖问题的参数化复杂度。我们观察到Langerman与Morin [Discrete & Computational Geometry 2005]在几何覆盖问题背景下提出的两种算法可适用于此设定，从而为半梯无超图中的集合覆盖问题提供了简单的固定参数可解（FPT）算法和核化算法。我们通过该问题的压缩下界补充了算法结果，该下界在标准复杂度理论假设下证明了核化的紧致性。