Evader Interdiction and Collateral Damage
In network interdiction problems, evaders (e.g., hostile agents or data packets) may be moving through a network towards targets and we wish to choose locations for sensors in order to intercept the evaders before they reach their destinations. 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 sensors placed to detect them. The challenge in such problems is to choose sensor locations economically, balancing security 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 optimal sensor placement algorithms for several classes of special graphs and hardness and approximation results for general graphs, including for deterministic or Markov chain-based and reactive or oblivious evaders. In a similar-sounding but fundamentally different problem setting posed by  where both evaders and innocent travelers are reactive, we again give optimal algorithms for special cases and hardness and approximation results on general graphs.
KeywordsMarkov Chain Target Node Vertex Cover Collateral Damage Chordal Graph
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- 1.Bar-Noy, A., Khuller, S., Schieber, B.: The complexity of finding most vital arcs and nodes. Technical report, University of Maryland, College Park, MD, USA (1995)Google Scholar
- 3.Even, G., Levi, R., Rawitz, D., Schieber, B., Shahar, S., Sviridenko, M.: Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs. ACM Transactions on Algorithms 4(3) (2008)Google Scholar
- 4.Even, S.: Graph Algorithms. Computer Science Press (1979)Google Scholar
- 7.Glazer, K., Rubinstein, A.: A study in the pragmatics of persuasion: A game theoretical approach. Theoretical Economics 1, 395–410 (2006)Google Scholar
- 8.Gutfraind, A., Ahmadizadeh, K.: Markovian Network Interdiction and the Four Color Theorem. Review with SIAM J. Discrete Math. (2009), http://arxiv.org/abs/0911.4322
- 9.Gutfraind, A., Hagberg, A., Izraelevitz, D., Pan, F.: Interdiction of a Markovian Evader. In: Dell, R., Wood, K. (eds.) Proc. INFORMS Computing Society Conference (January 2011)Google Scholar
- 12.Iwata, S., Nagano, K.: Submodular function minimization under covering constraints. In: FOCS, pp. 671–680 (2009)Google Scholar
- 15.Koufogiannakis, C., Young, N.E.: Greedy Δ-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5555, pp. 634–652. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 19.Pan, F., Charlton, W.S., Morton, D.P.: Interdicting smuggled nuclear material. In: Woodruff, D. (ed.) Network Interdiction and Stochastic Integer Programming, pp. 1–19. Kluwer Academic Publishers, Boston (2003)Google Scholar