Rerouting Flows When Links Fail

We introduce reroutable flows, a robust version of network flows in which link failures can be mitigated by rerouting the affected flow. An important new feature of this model, distinguishing it from existing robust network flow models, is that no flow can get lost in the network. Our goal is to compute maximum flows under this robustness requirement. We investigate different variants depending on the number of failing links, the capacities available for rerouting, and integrality requirements. While the most general versions of the model turn out to be NP-hard, we devise linear programming (LP) formulations and combinatorial algorithms for important special cases and provide approximation algorithms for the harder variants.