We study the parameterized complexity of interdiction problems in graphs. 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 shortest paths. 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.
Next, we show close relation between interdiction problems and partial cover
problems on bipartite graphs where the goal is not to cover all elements but to
minimize/maximize the number of covered elements with specific number of sets.
Hereby, we investigate the parameterized complexity of several partial cover
problems on bipartite graphs
