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

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.
978-3-319-63975-8
978-3-319-63976-5
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1214342
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact