Parameterized Complexity of Edge Interdiction Problems

For an optimization problem on edge-weighted graphs, the corresponding interdiction problem can be formulated as a game consisting of two players, namely, an interdictor and an evader, who compete on an objective with opposing interests. In an edge interdiction problem, every edge of the input graph is associated with an interdiction cost. The interdictor interdicts the graph by modifying the edges in the graph and the number of such modifications is bounded 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 study the parameterized complexity of edge interdiction problems related to minimum spanning tree, maximum matching, maximum flow and minimum maximal matching 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 reveal close relation between edge interdiction problems and partial covering problems on bipartite graphs.