Flow Augmentation - Solving edge cutting problems using a cutting-edge method

A recently developed method of reducing a minimal cut into a minimum cut solved a challenging generalization of the classical minimum cut problem. We show how to use this method in detail, along with a few solutions to (restricted version of) \(\ell\)-Bundled cut, \(\ell\)-chain SAT, and \(\ell\)-skew multicut. As many of the considered problems are NP-hard in general, we focus on parameterized complexity – solving them in \(f(\ell) \cdot n^{O(1)}\) for some computable function \(f\).