We show that two geometric cover problems in the plane, related to covering points with disjoint line segments, are NP-complete. Given $n$ points in the plane and a value $k$, the first problem asks if all points can be covered by $k$ disjoint line segments; the second problem treats the analogous question for $k$ guillotine cuts.

翻译：我们证明了平面中两个与使用互不相交线段覆盖点相关的几何覆盖问题是NP完全的。给定平面中的$n$个点和一个数值$k$，第一个问题询问是否所有点都能被$k$条互不相交的线段覆盖；第二个问题则针对$k$次断头台切割提出了类似的问题。