Combinatorial Bounds on Nonnegative Rank and Extended Formulations [article]

Samuel Fiorini and Volker Kaibel and Kanstantsin Pashkovich and Dirk Oliver Theis
2012 arXiv   pre-print
An extended formulation of a polytope P is a polytope Q which can be projected onto P. Extended formulations of small size (i.e., number of facets) are of interest, as they allow to model corresponding optimization problems as linear programs of small sizes. The main known lower bounds on the minimum sizes of extended formulations for fixed polytope P (Yannakakis 1991) are closely related to the concept of nondeterministic communication complexity. We study the relative power and limitations of the bounds on several examples.
arXiv:1111.0444v2 fatcat:c7buz47olnhkhfljt5uyisvsde