Layers and Matroids for the Traveling Salesman's Paths
Discrete Mathematics
2017-11-01 v3 Combinatorics
Abstract
Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive "generalized Gao-trees". We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the path TSP.
Keywords
Cite
@article{arxiv.1703.07170,
title = {Layers and Matroids for the Traveling Salesman's Paths},
author = {Frans Schalekamp and András Sebő and Vera Traub and Anke van Zuylen},
journal= {arXiv preprint arXiv:1703.07170},
year = {2017}
}