The K Critical Path Sets to Protect in Interdiction Networks under Limited Defensive Resources

This paper considers a network under intelligent threats. The defender of the network attempts to identify which disjoint K-critical path sets to be fortified under limited resources in order to better resist to attacks. Strengthening paths consists on increasing the path survivability by increasing individual survival probabilities of some or all arcs within the path accounting for limited resources. These resources are expressed through a defensive budget. The model assumes different reinforcement scenarios using different levels of resources. The paper proposes two solution methods. The first method maximizes the smallest survival probability over the K breakthrough paths to select under a budget constraint. The second one minimizes the cost of the overall survivability improvement while maintaining the smallest survival probability over the K selected breakthrough paths to a predefined threshold value. The formulated integer programs are solved optimally in a short time. This is the case even for large networks. The sensitivity analysis indicates in particular that, beyond some levels of defensive resources consumption, the survivability improvement becomes very slow suggesting an efficient re-allocation of the budget.