Extended Formulations, Nonnegative Factorizations, and Randomized Communication Protocols
نویسندگان
چکیده
We show that the binary logarithm of the non-negative rank of a non-negative 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.
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عنوان ژورنال:
- Math. Program.
دوره 153 شماره
صفحات -
تاریخ انتشار 2012