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Corpus ID: 221341075

On the Approximability of the Traveling Salesman Problem with Line Neighborhoods

@article{Antoniadis2020OnTA,
title={On the Approximability of the Traveling Salesman Problem with Line Neighborhoods},
author={A. Antoniadis and S{\'a}ndor Kisfaludi-Bak and B. Laekhanukit and D. Vaz},
journal={ArXiv},
year={2020},
volume={abs/2008.12075}
}

We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds for the problem in $\mathbb{R}^d$, with $d\ge 3$, are $\mathrm{NP}$-hardness and an $O(\log^3 n)$-approximation algorithm which is based on a reduction to the group Steiner tree problem.
We show that TSP with lines in $\mathbb{R}^d$ is APX-hard for any $d\ge… CONTINUE READING