Geospatial Abduction with Adaptive Adversaries

  • Paulo Shakarian
  • V. S. Subrahmanian
  • John P. Dickerson


In this chapter, we focus on the problem of geospatial abduction in the presence of an adversary who understands how we are reasoning about his behavior. For instance, consider an insurgent group carrying out Improvised Explosive Device (IED) attacks on US soldiers. Such an adversary may wish to carry out its attacks and select its cache locations (to support those attacks) in a way that it believes will most likely evade detection. How can an agent (e.g., US forces) anticipate this kind of reasoning by the adversary and find optimal locations to search for weapons caches? In this chapter, we develop a framework to express both the adversary’s problem and the agent’s problem via the paradigm of Stackelberg games. We formally specify the Optimal Adversary Strategy (OAS) problem, allowing the adversary to find a set of cache locations to minimize (what it believes) to be the probability of being discovered.We describe results on the computational complexity of OAS and algorithms to efficiently compute OAS. As the situation is modeled as a Stackelberg game, the agent (e.g., US forces) takes the final action (e.g., search for the IED caches). The agent can decide where to search after considering the space of options that the adversary has and after considering how the adversary might act in order to evade detection. We formalize this as the Maximal Counter- Adversary (MCA) strategy.We describe results on the computational complexity of MCA, as well as algorithms to efficiently compute MCA. These include algorithms that provide guaranteed polynomial approximations to MCA. We describe experimental results about the running time, accuracy, and quality of solutions found by the algorithms to compute OAS and MCA.


Reward Function Cutoff Distance Incremental Increase Stackelberg Game Cache Location 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Leyton-Brown, K., Shoham, Y. 2008. Essentials of Game Theory: A Concise, Multidisciplinary Introduction. Morgan and Claypool Publishers.Google Scholar
  2. 2.
    Johnson, D. 1982. The NP-Completeness Column: An Ongoing Guide. Journal of Algorithms 3, 2, 182–195.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Charnes, A., Cooper, W. 1962. Programming with linear fractional functionals. Naval Research Logistics Quarterly 9, 3, 163–297.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Karmarkar, N. 1984. A new polynomial-time algorithm for linear programming. Combinatorica 4, 4, 373–395.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Feige, U., Mirrokni, V. S., Vondrak, J. 2007. Maximizing non-monotone submodular functions. In FOCS 07: Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Washington, DC, USA, 461–471.Google Scholar
  6. 6.
    Feige, U. 1998. A threshold of ln n for approximating set cover. J. ACM 45, 4, 634–652.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Nemhauser, G., Wolsey, L., Fisher, M. 1978. An analysis of the approximations for maximizing submodular set functions. Mathematical Programming 14, 265–294.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Shakarian, P., Subrahmanian, V.S., Sapino, M.L. SCARE: A Case Study with Baghdad, Proc. 2009 Intl. Conf. on Computational Cultural Dynamics (eds. D. Nau, A. Mannes), Dec. 2009, AAAI Press.Google Scholar
  9. 9.
    Shakarian, P., Subrahmanian, V.S., Sapino, M.L. 2012. GAPS: Geospatial Abduction Problems, ACM Transactions on Intelligent Systems and Technology (TIST), 3, 1, to appear.Google Scholar
  10. 10.
    Shakarian, P., Subrahmanian, V.S. Region-based Geospatial Abduction with Counter-IED Applications, accepted for publication in:Wiil, U.K. (ed.).Counterterrorism and Open Source Intelligence, Springer Verlag Lecture Notes on Social Networks, to appear, 2011.Google Scholar
  11. 11.
    Shakarian, P., Nagel, M., Schuetzle, B., Subrahmanian, V.S. 2011. Abductive Inference for Combat: Using SCARE-S2 to Find High-Value Targets in Afghanistan, in Proc. 2011 Intl. Conf. on Innovative Applications of Arti cial Intelligence, Aug. 2011, AAAI Press.Google Scholar
  12. 12.
    Shakarian, P., Dickerson, J., Subrahmanian, V.S. 2012. Adversarial Geospatial Abduction Problems, ACM Transactions on Intelligent Systems and Technology (TIST), to appear.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Paulo Shakarian
    • 1
  • V. S. Subrahmanian
    • 2
  • John P. Dickerson
  1. 1.Kings Valley DriveBowieUSA
  2. 2.University of Maryland - College ParkPotomacUSA

Personalised recommendations