Parameterized covering in semi-ladder-free hypergraphs

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.