Optimal interdiction of unreactive Markovian evaders

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 increase the cost to an evader of traveling on a path through the network. Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not know all the roadblock locations or the best path to use for their escape. We introduce a model of network interdiction in which the motion of one or more evaders is described by Markov processes on a network and the evaders are assumed not to react to interdiction decisions. The interdiction objective is to find a node or set. of size at most B, that maximizes the probability of capturing the evaders. We prove that similar to the classical formulation this interdiction problem is NP-hard. But unlike the classical problem our interdiction problem is submodular and the optimal solution can be approximated within 1-lie using a greedy algorithm. Additionally. we exploit submodularity to introduce a priority evaluation strategy that speeds up the greedy algorithm by orders of magnitude. Taken together the results bring closer the goal of finding realistic solutions to the interdiction problem on global-scale networks