This chapter refers to a very interesting combinatorial object called permutahedron. We provide three different compact extended formulations. The first one is based on LP techniques and the second one on a simple projection of a polyhedron whose vertices are integral. Both these formulations require a quadratic number of variables and inequalities. A better compact extended formulation can be obtained via sorting networks for which a$$O(nlog n)$$ formulation can be given.

The Permutahedron

Lancia G.;Serafini P.
2018-01-01

Abstract

This chapter refers to a very interesting combinatorial object called permutahedron. We provide three different compact extended formulations. The first one is based on LP techniques and the second one on a simple projection of a polyhedron whose vertices are integral. Both these formulations require a quadratic number of variables and inequalities. A better compact extended formulation can be obtained via sorting networks for which a$$O(nlog n)$$ formulation can be given.
2018
978-3-319-63975-8
978-3-319-63976-5
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1214342
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