Minimum Constraint Removal Problem for Line Segments is NPhard
Abstract
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 collisionfree path. It has been proved that $MCR$ problem is $NPhard$ 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 NPhard for both weighted and unweighted line segments.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.03140
 Bibcode:
 2021arXiv210703140S
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Robotics;
 68XX;
 F.0;
 A.0