When a flow is not allowed to be reoriented the Maximum Residual Flow Problem with k-Arc Destruction is known to be NP-hard for k=2. We show that when a flow is allowed to be adaptive the problem becomes polynomial for every fixed k.
Cite
@article{arxiv.1711.00831,
title = {Adaptive Network Flow with $k$-Arc Destruction},
author = {Thomas Ridremont and Dimitri Watel and Pierre-Louis Poirion and Christophe Picouleau},
journal= {arXiv preprint arXiv:1711.00831},
year = {2017}
}