Hidden Vertices in Extensions of Polytopes
Combinatorics
2015-01-13 v2
Abstract
Some widely known compact extended formulations have the property that each vertex of the corresponding extension polytope is projected onto a vertex of the target polytope. In this paper, we prove that for heptagons with vertices in general position none of the minimum size extensions has this property. Additionally, for any d >= 2 we construct a family of d-polytopes such that at least 1/9 of all vertices of any of their minimum size extensions is not projected onto vertices.
Keywords
Cite
@article{arxiv.1404.2752,
title = {Hidden Vertices in Extensions of Polytopes},
author = {Kanstantsin Pashkovich and Stefan Weltge},
journal= {arXiv preprint arXiv:1404.2752},
year = {2015}
}
Comments
9 pages, to appear in: Operations Research Letters