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.
翻译:在最低限度限制清除($MCR$)中,没有可行的途径可以从起点走向目标,而且,为了找到一条无碰撞的道路,应该消除最低限度限制,已经证明,当限制有任意的形状,甚至有锥形多边形的形状时,$MCR$问题就是$NP-hard$,然而,当限制是线条,问题尚未解决到其他情况时,它有一个简单的线性解决办法。在本文中,通过减少子元件问题,分三个步骤,我们表明,对于加权和未加权线段来说,问题都很难解决。