Matroid-Based TSP Rounding for Half-Integral Solutions
Data Structures and Algorithms
2025-07-17 v2
Abstract
We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than-1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, and a new use of max-entropy sampling, can give better guarantees.
Cite
@article{arxiv.2111.09290,
title = {Matroid-Based TSP Rounding for Half-Integral Solutions},
author = {Anupam Gupta and Euiwoong Lee and Jason Li and Marcin Mucha and Heather Newman and Sherry Sarkar},
journal= {arXiv preprint arXiv:2111.09290},
year = {2025}
}