| Article ID: | iaor20003805 |
| Country: | Germany |
| Volume: | 86 |
| Issue: | 3 |
| Start Page Number: | 499 |
| End Page Number: | 514 |
| Publication Date: | Jan 1999 |
| Journal: | Mathematical Programming |
| Authors: | Boyd S., Carr R. |
| Keywords: | programming: linear |
Consider the 2-matching problem defined on the complete graph, with edge costs which satisfy the triangle inequality. We prove that the value of a minimum cost 2-matching is bounded above by 4/3 times the value of its linear programming relaxation, the fractional 2-matching problem. This lends credibility to a long-standing conjecture that the optimal value for the traveling salesman problem is bounded above by 4/3 times the value of its linear programming relaxation, the subtour elimination problem.