Mathematical Programming

, Volume 33, Issue 1, pp 43–60 | Cite as

Facets of the linear ordering polytope

  • Martin Grötschel
  • Michael Jünger
  • Gerhard Reinelt


LetD n be the complete digraph onn nodes, and letP LO n denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes ofD n (i.e. these are exactly the acyclic tournaments ofD n ). We show that various classes of inequalities define facets ofP LO n , e.g. the 3-dicycle inequalities, the simplek-fence inequalities and various Möbius ladder inequalities, and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input-output matrices, i.e. the solution of permutation resp. linear ordering problems.

Key words

Facets of Polyhedra Linear Ordering Problem Triangulation Problem Permutation Problem 


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Copyright information

© The Mathematical Programming Society, Inc. 1985

Authors and Affiliations

  • Martin Grötschel
    • 1
  • Michael Jünger
    • 1
  • Gerhard Reinelt
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgFR Germany

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