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Facets of the linear ordering polytope

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Abstract

LetD n be the complete digraph onn nodes, and letP nLO 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 nLO , 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.

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Lena Schlipf & Jens M. Schmidt

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Grötschel, M., Jünger, M. & Reinelt, G. Facets of the linear ordering polytope. Mathematical Programming 33, 43–60 (1985). https://doi.org/10.1007/BF01582010

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