A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP
Abstract
We show that for some $\epsilon > 10^{36}$ and any metric TSP instance, the max entropy algorithm returns a solution of expected cost at most $\frac{3}{2}\epsilon$ times the cost of the optimal solution to the subtour elimination LP. This implies that the integrality gap of the subtour LP is at most $\frac{3}{2}\epsilon$. This analysis also shows that there is a randomized $\frac{3}{2}\epsilon$ approximation for the 2edgeconnected multisubgraph problem, improving upon Christofides' algorithm.
 Publication:

arXiv eprints
 Pub Date:
 May 2021
 arXiv:
 arXiv:2105.10043
 Bibcode:
 2021arXiv210510043K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Mathematics  Combinatorics;
 Mathematics  Probability
 EPrint:
 Fix a missing case concerning the location of the root