A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP
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We show that for some ϵ > 10^-36 and any metric TSP instance, the max entropy algorithm returns a solution of expected cost at most 3/2-ϵ 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 3/2-ϵ. This analysis also shows that there is a randomized 3/2-ϵ approximation for the 2-edge-connected multi-subgraph problem, improving upon Christofides' algorithm.
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