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.File in questo prodotto:
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