We consider the general network information flow problem, which was
introduced by Ahlswede et. al. We show a periodicity effect: for
every integer m greater than 1, there exists an instance of the
network information flow problem that admits a solution if and only if
the alphabet size is a ... more >>>

We present improved algorithms for testing monotonicity of functions.
Namely, given the ability to query an unknown function $f$, where
$\Sigma$ and $\Xi$ are finite ordered sets, the test always accepts a
monotone $f$, and rejects $f$ with high probability if it is $\e$-far
from being monotone (i.e., every ... more >>>