In the minimum constraint removal problem, we are given a set of overlapping geometric objects as obstacles in the plane, and we want to find the minimum number of obstacles that must be removed to reach a target point t from the source point s by an obstacle-free path. The problem is known to be intractable and no sub-linear approximations are known even for simple obstacles such as rectangles and disks. The main result of our paper is an approximation framework that gives an $O(\sqrt{n\alpha (n)})$-approximation for polygonal obstacles, where $\alpha (n)$ denotes the inverse Ackermann's function. For pseudodisks and rectilinear polygons, the same technique achieves an $O(\sqrt{n})$-approximation. The technique also gives $O(\sqrt{n})$-approximation for the minimum color path problem in graphs. We also present some inapproximability results for the geometric constraint removal problem.

在最小的约束去除问题，我们给出了一组重叠的几何对象为在飞机上的障碍，我们希望找到的，必须去除，以达到目标点障碍物的最小数目牛逼从源点小号通过障碍无路径。已知该问题是棘手的，即使对于简单的障碍物（例如矩形和圆盘），也没有子线性近似值是已知的。本文的主要结果是一个近似框架，它给出了$Ø（\sqrt{ñ\alpha （ñ）}）$-多边形障碍物的近似值 $\alpha （ñ）$表示逆阿克曼函数。对于伪磁盘和直线多边形，相同的技术可以实现$Ø（\sqrt{ñ}）$-近似。该技术还给$Ø（\sqrt{ñ}）$-近似图中的最小颜色路径问题。我们还提出了一些关于几何约束消除问题的不近似结果。