Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman Problem

@article{Gutekunst2019CharacterizingTI,
  title={Characterizing the Integrality Gap of the Subtour LP for the Circulant Traveling Salesman Problem},
  author={Samuel C. Gutekunst and David P. Williamson},
  journal={ArXiv},
  year={2019},
  volume={abs/1902.06808}
}
We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is equal to an entirely combinatorial lower bound from Van der Veen, Van Dal, and Sierksma. We prove this conjecture by giving an explicit optimal solution to the subtour LP. We then use it to show that the integrality gap of the subtour LP is 2 on circulant… CONTINUE READING
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