We study a class of geometric covering and packing problems for bounded closed regions on the plane. We are given a set of axis-parallel line segments that induce a planar subdivision with bounded (rectilinear) faces. We are interested in the following problems.

(P1) Stabbing-Subdivision:

Stab all closed bounded faces of the planar subdivision by selecting a minimum number of points in the plane.

(P2) Independent-Subdivision:

Select a maximum size collection of pairwise non-intersecting closed bounded faces of the planar subdivision.

(P3) Dominating-Subdivision:

Select a minimum size collection of bounded faces of the planar subdivision such that every other face of the subdivision that is not selected has a non-empty intersection (i.e., sharing an edge or a vertex) with some selected face.

我们研究了平面上有界封闭区域的一类几何覆盖和堆积问题。我们给出了一组轴平行线段，这些线段诱导出带有有界（直线）面的平面细分。我们对以下问题感兴趣。

（P1）刺刺细分：

通过选择平面中最小数量的点，刺入平面细分的所有闭合有界面。

（P2）独立细分：

选择平面细分的成对不相交的闭合有界面的最大尺寸集合。

（P3）支配细分：

选择平面细分的有界面的最小尺寸集合，以使未被选择的细分的每个其他面与某个选定面具有非空相交（即，共享一条边或一个顶点）。