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Not Every GTSP Facet Induces an STSP Facet

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Book cover Integer Programming and Combinatorial Optimization (IPCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3509))

Abstract

The graphical traveling salesman problem (GTSP) has been studied as a variant of the classical symmetric traveling salesman problem (STSP) suited particularly for sparse graphs. In addition, it can be viewed as a relaxation of the STSP and employed for solving the latter to optimality as originally proposed by Naddef and Rinaldi. There is a close natural connection between the two associated polyhedra. Until now, it was not known whether there are facets in TT-form of the GTSP polyhedron which are not facets of the STSP polytope as well. In this paper we give an affirmative answer to this question for n ≥ 9 and provide a general method for constructing such facets.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Marcus Oswald, Gerhard Reinelt & Dirk Oliver Theis

Authors
  1. Marcus Oswald
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  2. Gerhard Reinelt
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  3. Dirk Oliver Theis
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln,  

    Michael Jünger

  2. Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Volker Kaibel

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© 2005 Springer-Verlag Berlin Heidelberg

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Oswald, M., Reinelt, G., Theis, D.O. (2005). Not Every GTSP Facet Induces an STSP Facet. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_34

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  • DOI: https://doi.org/10.1007/11496915_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26199-5

  • Online ISBN: 978-3-540-32102-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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