We give a review of results on the minimum convex cover and maximum hidden set problems. In addition, we give some new results. First we show that it is NP-hard to determine whether a polygon has the same convex cover number as its hidden set number. We then give some important examples in which these quantities don't always coincide. Finally, We present some consequences of insights from Browne, Kasthurirangan, Mitchell and Polishchuk [FOCS, 2023] on other classes of simple polygons.

翻译：本文综述了最小凸覆盖与最大隐藏集问题的相关研究成果，并给出若干新结论。首先证明：判定一个多边形是否具有与其隐藏集数相等的凸覆盖数是NP困难的。随后给出关键反例表明这两个量并非总是相等。最后，基于Browne、Kasthurirangan、Mitchell与Polishchuk[FOCS, 2023]的研究洞见，推导了关于其他简单多边形类的一些推论。