Minimum Constraint Removal Problem for Line Segments is NP-hard

07/07/2021

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by   Bahram Sadeghi Bigham, et al.

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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.