Minimum Constraint Removal Problem for Line Segments is NP-hard
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 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.03140
- arXiv:
- arXiv:2107.03140
- Bibcode:
- 2021arXiv210703140S
- Keywords:
-
- Computer Science - Computational Geometry;
- Computer Science - Robotics;
- 68-XX;
- F.0;
- A.0
- E-Print:
- Bigham, Bahram Sadeghi. "Minimum constraint removal problem for line segments is NP-hard." Discrete Mathematics, Algorithms and Applications (2022): 2250055