We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(\log\log n)$. The results are based on a new form of recursive partitioning in the plane, in which faces that are constant-complexity and orthogonally convex are recursively partitioned into a constant number of such faces.

翻译：我们给出一个多元时常量近似算法, 用于为( 轴对齐) 矩形设定的最大独立值。 使用一个多边时算法, 先前已知的最佳近似系数是$O (\log\log n) 。 结果基于在平面上的一种新形式的递转分隔, 即常复和正陈形面部被循环分割成一定数量的此类面部 。