In a standard Ford-Fulkerson setting (directed graph $G$ with a source $s$ and a sink $t$), consider the problem of achieving a given amount of flow using the minimum number of nodes in the graph.
The familiarity with the problem discussed here: Laying paths on a network using minimum number of links/edges seems to suggest that this problem might also be NP-hard. I can split every node in $G$ into two nodes and add an edge of unit cost between them, and assign zero cost to all the original edges. Cap-SNDP (http://www.cis.upenn.edu/~sanjeev/papers/ipco11_capacitated.pdf) on this new graph is equivalent to finding the minimum number of nodes in $G$ required to support the desired flow.
1) Is this problem known to be NP-hard?
2) If I restrict attention to layered graphs, does it change anything about the complexity/approximability? (A layered graph is one in which all $s-t$ paths have the same number of edges.)
Thanks in advance.