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arXiv · 2105.10043

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

Anna Karlin·Nathan Klein·Shayan Oveis Gharan
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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 2-edge-connected multi-subgraph problem, improving upon Christofides' algorithm.

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Anna Karlin, Nathan Klein, Shayan Oveis Gharan. 2021-05-20. A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP. https://arxiv.org/abs/2105.10043

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