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- W4301915202 abstract "Determining the precise integrality gap for the subtour LP relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years in the general case of symmetric costs that obey triangle inequality. Boyd and Carr [3] observe that we do not even know the worst-case upper bound on the ratio of the optimal 2-matching to the subtour LP; they conjecture the ratio is at most 10/9. In this paper, we prove the Boyd-Carr conjecture. In the case that a fractional 2-matching has no cut edge, we can further prove that an optimal 2-matching is at most 10/9 times the cost of the fractional 2-matching." @default.
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- W4301915202 date "2011-07-08" @default.
- W4301915202 modified "2023-09-23" @default.
- W4301915202 title "A Proof of the Boyd-Carr Conjecture" @default.
- W4301915202 doi "https://doi.org/10.48550/arxiv.1107.1628" @default.
- W4301915202 hasPublicationYear "2011" @default.
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