Evader interdiction: algorithms, complexity and collateral damage

Abstract

In network interdiction problems, evaders (e.g., hostile agents or data packets) are moving through a network toward targets and we wish to choose locations for sensors in order to intercept the evaders. The evaders might follow deterministic routes or Markov chains, or they may be reactive, i.e., able to change their routes in order to avoid the sensors. The challenge in such problems is to choose sensor locations economically, balancing interdiction gains with costs, including the inconvenience sensors inflict upon innocent travelers. We study the objectives of (1) maximizing the number of evaders captured when limited by a budget on sensing cost and, (2) capturing all evaders as cheaply as possible. We give algorithms for optimal sensor placement in several classes of special graphs and hardness and approximation results for general graphs, including evaders who are deterministic, Markov chain-based, reactive and unreactive. A similar-sounding but fundamentally different problem setting was posed by Glazer and Rubinstein where both evaders and innocent travelers are reactive. We again give optimal algorithms for special cases and hardness and approximation results on general graphs.

A Decomposition Approach for Stochastic Shortest-Path Network Interdiction with Goal Threshold

“…Stochastic models are more realistic to real-world scenarios and can invariably address the uncertainty in the network structure and evader behavior. Johnson et al [29] further provided algorithms for optimal sensor placement in several classes of special graphs and approximation results for general graphs, assuming that the evaders are deterministic, Markov chain-based, reactive, and unreactive. Similar to our model, Bertsimas et al [30] also introduced the randomized network interdiction problem, which allows the interdictor to use randomness to select arcs to be removed.…”