Robustifying networks for flow problems against edge failure
Abstract
We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version is a saddle-point problem with discrete variables. We present two approaches for the solution of the robust network flow problem. One way is to formulate the problem as a bigger linear program. The other is to solve a multi-level optimization problem, where the linear programs appearing at the lower level can be solved by the dual simplex method with a warm start. We then consider the problem of robustifying the network. This is accomplished by optimally using a fixed budget for strengthening certain edges, i.e., increasing their capacity. This problem is solved by a sequence of linear programs at the upper level, while at the lower levels the mentioned dual simplex algorithm is employed.
Cite
@article{arxiv.2504.17031,
title = {Robustifying networks for flow problems against edge failure},
author = {Artyom Klyuchikov and Roland Hildebrand and Sergei Protasov and Alexander Rogozin and Alexei Chernov},
journal= {arXiv preprint arXiv:2504.17031},
year = {2025}
}