We prove an optimal $\Omega(n)$ lower bound on the randomized
communication complexity of the much-studied
Gap-Hamming-Distance problem. As a consequence, we
obtain essentially optimal multi-pass space lower bounds in the
data stream model for a number of fundamental problems, including
the estimation of frequency moments.

The Gap-Hamming-Distance problem is a ... more >>>

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate non-negative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term.
The logarithm of the nonnegative rank is known to ... more >>>