Extended formulations, nonnegative factorizations, and randomized communication protocols

Authors:
Yuri Faenza;Samuel Fiorini;Roland Grappe;Hans Raj Tiwary
Affiliations:
Dipartimento di Matematica Pura e Applicata, Università di Padova, Padova, Italy;Département de Mathématique, Université Libre de Bruxelles, Brussels, Belgium;Laboratoire d'Informatique de Paris-Nord, UMR CNRS 7030, Institut Galilée, Université Paris-Nord, Villetaneuse, France;Département de Mathématique, Université Libre de Bruxelles, Brussels, Belgium
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

We show that the binary logarithm of the nonnegative rank of a nonnegative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new conditional lower bounds on the sizes of extended formulations, in particular, for perfect matching polytopes.