Article révisé par les pairs
Résumé : 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. © 2012 Springer-Verlag.