Title | ||
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2-Matchings, the Traveling Salesman Problem, and the Subtour LP: A Proof of the Boyd-Carr Conjecture. |
Abstract | ||
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Determining the precise integrality gap for the subtour linear programming (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 [Boyd S, Carr R (2011) Finding low cost TSP and 2-matching solutions using certain half-integer subtour vertices. Discrete Optim. 8:525-539. Prior version accessed June 27, 2011, http://www.site.uottawa.ca/(similar to)sylvia/recentpapers/halftri.pdf.] 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 the support of a fractional 2-matching has no cut edge, we can further prove that an optimal 2-matching has cost at most 10/9 times the cost of the fractional 2-matching. |
Year | DOI | Venue |
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2014 | 10.1287/moor.2013.0608 | MATHEMATICS OF OPERATIONS RESEARCH |
Keywords | DocType | Volume |
traveling salesman problem,subtour elimination,linear programming,integrality gap,2-matching,fractional 2-matching | Journal | 39 |
Issue | ISSN | Citations |
2 | 0364-765X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Frans Schalekamp | 1 | 76 | 7.91 |
David P. Williamson | 2 | 3564 | 413.34 |
Anke Van Zuylen | 3 | 291 | 22.10 |