In a flow network, suppose we add constraints of the following type:
The flow entering a vertex $v$ must be at most the flow exiting a vertex $u$.
Is maximum-flow with such constraints still solvable in polynomial time?
Is it possible to reduce it to a standard maximum-flow problem?
NOTE: I found a recent paper that studies network flow with constraints, however, the constraints studied there are different:
"A negative disjunctive constraint states that a certain pair of arcs cannot be simultaneously used for sending flow"
"A positive disjunctive constraint forces that for certain pairs of arcs at least one arc has to carry flow".