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Minimum Constraint Removal Problem for Line Segments is NP-hard

2021-07-07 10:57:22
Bahram Sadeghi Bigham
arXiv_RO
 
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.

Abstract (translated)

URL

https://arxiv.org/abs/2107.03140

PDF

https://arxiv.org/pdf/2107.03140.pdf

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