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Mathematical Programming

, Volume 33, Issue 1, pp 1–27 | Cite as

The traveling salesman problem on a graph and some related integer polyhedra

  • Gérard Cornuéjols
  • Jean Fonlupt
  • Denis Naddef
Article

Abstract

Given a graphG = (N, E) and a length functionl: E → ℝ, the Graphical Traveling Salesman Problem is that of finding a minimum length cycle goingat least once through each node ofG. This formulation has advantages over the traditional formulation where each node must be visited exactly once. We give some facet inducing inequalities of the convex hull of the solutions to that problem. In particular, the so-called comb inequalities of Grötschel and Padberg are generalized. Some related integer polyhedra are also investigated. Finally, an efficient algorithm is given whenG is a series-parallel graph.

Key words

Traveling Salesman Problem Integer Polyhedron Facet Graph Series-Parallel Graph Steiner Tree Polynomial Algorithm 

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Copyright information

© The Mathematical Programming Society, Inc. 1985

Authors and Affiliations

  • Gérard Cornuéjols
    • 1
  • Jean Fonlupt
    • 2
  • Denis Naddef
    • 2
  1. 1.Graduate School of Industrial AdministrationCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Laboratoire d'Informatique et de Mathématiques Appliquées de GrenobleUniversity of GrenobleSaint Martin d'Hères CedexFrance

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