Rapidly computing robust minimum capacity s-t cuts: a case study in solving a sequence of maximum flow problems

The Minimum Capacity s-t Cut Problem (MinCut) is an intensively studied problem in combinatorial optimization. A natural extension is the problem of choosing a minimum capacity s-t cut when arc capacities are unknown but confined to known intervals. This motivates the Robust Minimum Capacity s-t Cut Problem (RobuCut), which has applications such as open-pit mining and project scheduling. In this paper, we show how RobuCut can be reduced to solving a sequence of maximum flow problems and provide an efficient algorithm for rapidly solving this sequence of problems. We demonstrate that our algorithm solves instances of RobuCut in seconds that would require hours if a standard maximum flow solver is iteratively used as a black-box subroutine.