The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling on a path through the network. Our wo...

We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum profit that can be obtained from shipping commodities across the network. The attacker is assumed to have some budget for destroying (or “interdicting”) arcs, and each arc is associated with a positive interdiction expense. In this pap...

This definition is unnecessarily restrictive— for instance, it should also include ship-based firepower—but the essence is reasonable: interdiction connotes preemptive attacks that limit an enemy’s subsequent ability to wage war, or carry out other nefarious activities. The mathematical study of interdiction has focused primarily on network interdiction, in which an enemy’s activities are model...

Shortest path network interdiction is a combinatorial optimization problem on an activity network arising in a number of important security-related applications. It is classically formulated as a bilevel maximin problem representing an “interdictor” and an “evader”. The evader tries to move from a source node to the target node along a path of the least cost while the interdictor attempts to fr...

Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been studied for a wide variety of classical combinatorial optimization problems, including maximum s-t flows, shortest s-t paths, maximum weight matchings, mini...

In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove a set of k matrix columns that minimizes in the residual matrix the sum of the row values, where the value of a row is defined to be the largest entry in that row. This combinatorial problem is closely related to bipartite network interdiction problem that can be applied to minimize th...

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 w...