Smallest Compact Formulation for the Permutahedron
Name
permutahedron-mp-rev.pdf
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227.45 KB
Format
Adobe PDF
Checksum (MD5)
a042bebd5dda8e1bfca2a2c97b3c33c7
Author(s)
Goemans, Michel X.
Date Issued
February 2014
Journal
Mathematical Programming
Publisher
Springer-Verlag
Citation
Goemans, Michel X. “Smallest Compact Formulation for the Permutahedron.” Mathematical Programming (2014): n. pag.
Version
Author's final manuscript
Abstract
In this note, we consider the permutahedron, the convex hull of all permutations of {1,2…,n} . We show how to obtain an extended formulation for this polytope from any sorting network. By using the optimal Ajtai–Komlós–Szemerédi sorting network, this extended formulation has Θ(nlogn) variables and inequalities. Furthermore, from basic polyhedral arguments, we show that this is best possible (up to a multiplicative constant) since any extended formulation has at least Ω(nlogn) inequalities. The results easily extend to the generalized permutahedron.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-014-0757-1
