Parameterized Complexity of Edge Interdiction Problems

We study the parameterized complexity of graph interdiction problems. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who compete on an objective with opposing interests. In edge interdiction problems, every edge of the input graph has an interdiction cost associated with it and the interdictor interdicts the graph by modifying the edges in the graph, and the number of such modifications is constrained by the interdictor’s budget. The evader then solves the given optimization problem on the modified graph. The action of the interdictor must impede the evader as much as possible. We focus on edge interdiction problems related to minimum spanning tree, maximum matching and maximum flow problems. These problems arise in different real world scenarios. We derive several fixed-parameter tractability and W[1]-hardness results for these interdiction problems with respect to various parameters. Hereby, we show close relation between edge interdiction problems and partial covering problems on bi-