Multicommodity Flow in Polynomial Time

@article{Hemmecke2009MulticommodityFI,
  title={Multicommodity Flow in Polynomial Time},
  author={Raymond Hemmecke and Shmuel Onn and Robert Weismantel},
  journal={CoRR},
  year={2009},
  volume={abs/0906.5106}
}
The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising polynomial time solvability of the problem in two broad situations.