In the minimum constraint removal ($MCR$), there is no feasible path to move from the starting point towards the goal and, the minimum constraints should be removed in order to find a collision-free path. It has been proved that $MCR$ problem is $NP-hard$ when constraints have arbitrary shapes or even they are in shape of convex polygons. However, it has a simple linear solution when constraints are lines and the problem is open for other cases yet. In this paper, using a reduction from Subset Sum problem, in three steps, we show that the problem is NP-hard for both weighted and unweighted line segments.

中文翻译：

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线段的最小约束去除问题是 NP-hard

在最小约束去除（$MCR$）中，没有从起点到目标的可行路径，为了找到无碰撞路径，应该去除最小约束。已经证明，当约束具有任意形状甚至是凸多边形时，$MCR$ 问题是$NP-hard$。然而，当约束是线并且问题在其他情况下是开放的时，它有一个简单的线性解决方案。在本文中，使用子集和问题的约简，分三步，我们表明该问题对于加权和未加权的线段都是 NP-hard 问题。