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Partial linear characterizations of the asymmetric travelling salesman polytope

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Abstract

We consider the linear programming formulation of the asymmetric travelling salesman problem. Several new inequalities are stated which yield a sharper characterization in terms of linear inequalities of the travelling salesman polytope, i.e., the convex hull of tours.

In fact, some of the new inequalities as well as some of the well-known subtour elimination constraints are indeed facets of the travelling salesman polytope, i.e., belong to the class of inequalities that uniquely characterize the convex hull of tours to an-city problem.

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References

  1. E. Balas, and M.W. Padberg: “On the facial structure of the travelling salesman polytope”, Carnegie-Mellon University, Pittsburgh, U.S.A., (April, 1973), unpublished.

    Google Scholar 

  2. V. Chvatal, “Edmonds polytopes and weekly hamiltonian graphs”,Mathematical Programming 5 (1973) 29–40.

    Google Scholar 

  3. G. Dantzig, R. Fulkerson and S. Johnson: “Solution of a large-scale travelling-salesman problem”,Operations Research 2 (1954) 393–410.

    Google Scholar 

  4. R. Garfinkel, and G.L. Nemhauser,Integer programming (Wiley, New York, 1972).

    Google Scholar 

  5. M. Grotschel and M.W. Padberg, “Lineare Charakterisierungen von Travelling Salesman Problemen”,Zeitschrift fur Operations Research, to appear.

  6. I. Heller, “On the problem of shortest path between points”, I and II,Bulletin of the American Mathematical Society 59 (1953) 551–552 (abstract).

    Google Scholar 

  7. H.W. Kuhn, “On certain convex polyhedra”,Bulletin of the American Mathematical Society 61 (1955) 557–558 (abstract).

    Google Scholar 

  8. M.W. Padberg and M.R. Rao, “The travelling salesman problem and a class of polyhedra of diameter two”,Mathematical Programming 7 (1974) 32–45.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Ökonometrie und Operations Research, Universität Bonn, West Germany

    Martin Grötschel

  2. Graduate School of Business Administration, New York University, New York, N.Y., USA

    Manfred W. Padberg

Authors
  1. Martin Grötschel
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  2. Manfred W. Padberg
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Grötschel, M., Padberg, M.W. Partial linear characterizations of the asymmetric travelling salesman polytope. Mathematical Programming 8, 378–381 (1975). https://doi.org/10.1007/BF01580454

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  • DOI: https://doi.org/10.1007/BF01580454

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