Network interdiction – models, applications, unexplored directions

Network interdiction is the monitoring or halting of an adversary’s activity on a network. Its models involve two players, usually called the interdictor and the evader (or, in the more general context of Stackelberg games, leader and follower). The evader operates on the network to optimize some objective such as moving through the network as fast as possible (shortest path interdiction), or with as little probability of being detected as possible (most reliable path interdiction), or to maximize the amount of goods transported through the network (network flow interdiction). The interdictor has the capacity to change the structure or parameters of the network (remove vertices or edges, increase detection probabilities, or lower arc capacities) in order to minimize the evader’s objective function. The study of network interdiction began with military applications: disruption of the flow of enemy troops. More recent applications include infectious disease control, counter-terrorism, interception of contraband and illegal items such as drugs, weapons, or nuclear material, and the monitoring of computer networks. A large variety of models have been proposed for different interdiction problems. These include combinatorial optimization, stochastic programming, and game theoretic approaches. In this note we attempt to collect the most researched models, match them with applications, and summarize the latest algorithmic and complexity results. In Section 1 we introduce the basic ideas and define the necessary terms. Section 2 is concerned with various models that have been proposed in the literature, as well as with algorithms and complexity bounds. In Section 3 we examine which models would be appropriate for which applications. Finally, in Section 4 we outline two promising research directions for the future.