We investigate the problem of partitioning a rectilinear polygon P with n vertices and no holes into rectangles using disjoint line segments drawn inside P under two optimality criteria. In the minimum ink partition, the total length of the line segments drawn inside P is minimized. We present an $O(n^3)$-time algorithm using $O(n^2)$ space that returns a minimum ink partition of P. In the thick partition, the minimum side length over all resulting rectangles is maximized. We present an $O(n^3{\log }^{2}n)$-time algorithm using $O(n^3)$ space that returns a thick partition using line segments incident to vertices of P, and an $O(n^6{\log }^{2}n)$-time algorithm using $O(n^6)$ space that returns a thick partition using line segments incident to the boundary of P. We also show that if the input rectilinear polygon has holes, the corresponding decision problem for the thick partition problem using line segments incident to vertices of the polygon is NP-complete. We also present an $O(m^3)$-time 3-approximation algorithm for the minimum ink partition for a rectangle containing m point holes.

我们研究了在两个最优性标准下使用在P内部绘制的不相交线段将具有n个顶点且没有孔的直线多边形P划分为矩形的问题。在最小墨水分区中，在P内绘制的线段的总长度被最小化。我们提出一个$○(n^{\mathrm{3个}})$-时间算法使用$○(n^{\mathrm{2个}})$返回P的最小墨水分区的空间。在厚分区中，所有生成的矩形的最小边长被最大化。我们提出一个$○(n^{\mathrm{3个}}{\mathrm{日志}}^{\mathrm{2个}}n)$-时间算法使用$○(n^{\mathrm{3个}})$使用入射到P的顶点的线段返回厚分区的空间，以及$○(n^{\mathrm{6个}}{\mathrm{日志}}^{\mathrm{2个}}n)$-时间算法使用$○(n^{\mathrm{6个}})$使用入射到P边界的线段返回厚分区的空间。我们还表明，如果输入的直线多边形有孔，则使用线段入射到多边形顶点的厚分区问题的相应决策问题是 NP 完全问题。我们还提出了一个$○({米}^{\mathrm{3个}})$包含m个点孔的矩形的最小墨水分区的 -time 3-approximation 算法。