# A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP

@article{Karlin2021AI, title={A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP}, author={A. Karlin and Nathan Klein and S. Gharan}, journal={ArXiv}, year={2021}, volume={abs/2105.10043} }

We show that for some e > 10−36 and any metric TSP instance, the max entropy algorithm returns a solution of expected cost at most 2 − e 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 2 − e. This analysis also shows that there is a randomized 2 − e approximation for the 2-edgeconnected multi-subgraph problem, improving upon Christofides’ algorithm. *karlin@cs.washington.edu. Research supported by Air Force… Expand

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