Beating the integrality ratio for s-t-tours in graphs
Abstract
Among various variants of the traveling salesman problem, the s-t-path graph TSP has the special feature that we know the exact integrality ratio, 3/2, and an approximation algorithm matching this ratio. In this paper, we go below this threshold: we devise a polynomial-time algorithm for the s-t-path graph TSP with approximation ratio 1.497. Our algorithm can be viewed as a refinement of the 3/2-approximation algorithm by Seb\H{o} and Vygen [2014], but we introduce several completely new techniques. These include a new type of ear-decomposition, an enhanced ear induction that reveals a novel connection to matroid union, a stronger lower bound, and a reduction of general instances to instances in which s and t have small distance (which works for general metrics).
Cite
@article{arxiv.1804.03112,
title = {Beating the integrality ratio for s-t-tours in graphs},
author = {Vera Traub and Jens Vygen},
journal= {arXiv preprint arXiv:1804.03112},
year = {2018}
}