Minimax problem of suppressing a communication network

The classical Ford and Fulkerson maximum flow problem in a directed network is generalized for the case when an attacker is able to reduce the capacity of network edges. The interference is to reduce the capacity of each edge rather than to reduce the flow through it; in the general case, this leads to the problem of minimizing the capacity of the minimum cut, which is reduced to a sequence of mathematical programming problems. Since the set of cuts can be identified with the set of all subsets of the set of network nodes, the resulting problem is equivalent to a discrete problem on a Boolean lattice, and it can be solved using submodular programming techniques developed in the works by Khachaturov. Numerical examples are presented.