We show that the problem of covering a set of points in the plane with a minimum number of guillotine cuts is NP-complete. To that end, first we present a new NP-completeness proof for the problem of covering points with disjoint line segments. Then, we adapt the proof to show that the problem remains NP-complete when the segments are guillotine cuts.

翻译：本文证明了在平面上用最少数量的断头台切割覆盖点集的问题是NP完全的。为此，我们首先针对用不相交线段覆盖点的问题提出了一种新的NP完全性证明。随后，我们调整该证明，表明当线段为断头台切割时，该问题仍然是NP完全的。