Combinatorial Bounds on Nonnegative Rank and Extended Formulations

2011/11/02 by Samuel Fiorini, Volker Kaibel, Fiorini, Samuel +5 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO

paper · pdf · doi:10.48550/arxiv.1111.0444

Revision, 25pp

arxiv created 2012/07/09 · arxiv updated 2012/07/10

Abstract

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.

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