We compare two multicommodity flow problems, the maximum sum of
flow, and the maximum concurrent flow. We show that, for a given
graph and a given set of $k$ commodities with specified demands, if
the minimum capacity of a multicut is approximated by the maximum
sum of flow within a factor of $\alpha$, for any subset of
commodities, then the minimum cut ratio is approximated by the
maximum concurrent flow within a factor of $O(\alpha\ln k)$.
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