ON THE COMPLEXITY OF TIMETABLE AND MULTI-COMMODITY FLOW PROBLEMS
there's a proof that the multi-commodity is NP-hard.
Multicommodity flows over time: Efficient algorithms and complexity
authors states that "[...] the only known polynomial-time algorithms for static multicommodity flow computations require general linear programming techniques".
They use word "static" only to differ from its time-dependent version. But I think it is the same problem considered in the first paper. Authors also refer to its complexity with the wording "poly($\simeq$LP)".
Can someone help me understand the right way of reading this apparent contradiction?