Extended Formulations for Polygons
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454_2012_Article_9421.pdf
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Author(s)
Fiorini, Samuel
Tiwary, Hans Raj
Rothvoss, Thomas
Date Issued
March 2012
Journal
Discrete & Computational Geometry
Publisher
Springer-Verlag
Citation
Fiorini, Samuel, Thomas Rothvoß, and Hans Raj Tiwary. “Extended Formulations for Polygons.” Discrete & Computational Geometry 48, no. 3 (March 16, 2012): 658–668.
Version
Author's final manuscript
Abstract
The extension complexity of a polytope P is the smallest integer k such that P is the projection of a polytope Q with k facets. We study the extension complexity of n-gons in the plane. First, we give a new proof that the extension complexity of regular n-gons is O(log n), a result originating from work by Ben-Tal and Nemirovski (Math. Oper. Res. 26(2), 193–205, 2001). Our proof easily generalizes to other permutahedra and simplifies proofs of recent results by Goemans (2009), and Kaibel and Pashkovich (2011). Second, we prove a lower bound of √(2n) on the extension complexity of generic n-gons. Finally, we prove that there exist n-gons whose vertices lie on an O(n)×O(n[superscript 2]) integer grid with extension complexity Ω(√/n./(√(log n))).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00454-012-9421-9
