A note on the traveling salesman problem

Authors:
V. Chvátal
Affiliations:
Institut für Ökonometrie und Operations Research, Rheinische Friedrich-Wilhelms-Universität, Bonn, Federal Republic of Germany
Venue:
Operations Research Letters
Year:
1989

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Abstract

We observe that (i) the problem of recognizing instances of the traveling salesman problem for which the subtour relaxation has an integer optimal solution is NP-complete and (ii) there is no nontrivial upper bound on the 'relative error' with which the optimal value of the TSP is approximated by the optimal value of its subtour relaxation.