Infoscience

Conference paper

# Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols

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.