Minimum constraint removal problem for line segments is NP-hard

In the minimum constraint removal (MCR), there is no feasible path to move from a 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.