The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme
Abstract
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04).
Cite
@article{arxiv.1112.0699,
title = {The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme},
author = {Yair Bartal and Lee-Ad Gottlieb and Robert Krauthgamer},
journal= {arXiv preprint arXiv:1112.0699},
year = {2016}
}