# 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.

## Keywords

Network interdiction Bridge policy Submodular set cover Markov chain Minimal cut Four color theorem## Notes

### Acknowledgements

We thank Amotz Bar-Noy and Rohit Parikh for useful discussions and two anonymous reviewers for valuable criticism. This work was funded by the Department of Energy at the Los Alamos National Laboratory through the LDRD program, and by the Defense Threat Reduction Agency. AG would like to thank Robert Kleinberg for fascinating lectures, and Feng Pan and Aric Hagberg for the support.

Some of the above results appeared as an extended abstract in the Proceedings of the 7th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (ALGOSENSORS) 2011. We have added proofs to many of the theorems and Theorem 6, which establishes a connection from Network Interdiction to graph coloring.

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