1NP-Hardness proof dropped for brevity. It can be shown that the Set Cover problem can be reduced to Problem 2. In particular, we are looking for a subset of flows $\gamma \subseteq \pmb{\mathrm{F}}$ with minimum total remaining data units where there exists a path from $s_{N+1}$ to $t_{N+1}$ removing all edges that have a flow in $\pmb{\mathrm{F}}-\gamma$.