Abstract.
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.
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Received August 26, 1996 / Revised version received July 6, 1999¶ Published online September 15, 1999
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Boyd, S., Carr, R. A new bound for the ratio between the 2-matching problem and its linear programming relaxation. Math. Program. 86, 499–514 (1999). https://doi.org/10.1007/s101079900102
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DOI: https://doi.org/10.1007/s101079900102