, Volume 81, Issue 1, pp 37–53 | Cite as

Geographic characteristics of a network interdiction problem

  • Irene Casas
  • Eric Delmelle
  • Justin Yates


The protection of critical infrastructure from natural and intentional events is a key component of any national security agenda. Protection schemes need to be readily identifiable and adaptable to complex changing environments. In this paper, we identify strategic geographic characteristics that impact the location of detection resources (e.g. sensors) towards the defense of regional critical infrastructure. Specifically, we seek to estimate the relationship between the results of a variation of the traditional shortest path network interdiction problem and geographical characteristics of the transportation infrastructure and the urban environment. Experiments conducted on three distinct transportation networks of different shapes and granularities (New York City—grid, Houston—radial, Boston—hybrid) underline the importance of geographic characteristics such as the proximity to resource location, attacker entry points as well as network coverage. Insights gained from this work are relevant to policy and decision makers to facilitate the development of analytical and decision-support tools capable of identifying resource allocation strategies. We discuss a heuristic-based framework that prioritizes the selection of detection resources, reflecting the importance of geographic characteristics. The findings underline the importance of geographical characteristics for the allocation of resources in a regional setting.


Critical infrastructure Geographic characteristics GIS Network interdiction problem Spatial optimization 


  1. Bard, J. (1998). Practical bilevel optimization: Algorithms and applications. Boston: Kluwer.CrossRefGoogle Scholar
  2. Bayrak, H., & Baily, M. (2008). Shortest path network interdiction with asymmetric information. Networks, 52(3), 133–140.CrossRefGoogle Scholar
  3. Brown, G., Carlyle, M., Salmeron, J., & Wood, K. (2006). Defending critical infrastructure. Interfaces, 36(6), 530–544.CrossRefGoogle Scholar
  4. Cameron, A., & Trivedi, P. (1998). Regression analysis of count data. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Church, R., & ReVelle, C. S. (1976). Theoretical and computational links between the p-median location set-covering and the maximal covering location problem. Geographical Analysis, 8(4), 406–415.CrossRefGoogle Scholar
  6. Church, R. L., & Scaparra, M. P. (2007). Protecting critical assets: The r-interdiction median problem with fortification. Geographical Analysis, 39(2), 129–146.CrossRefGoogle Scholar
  7. Church, R., Scaparra, M. P., & Middleton, R. S. (2004). Identifying critical infrastructure: The median and covering facility interdiction problems. Annals of the Association of American Geographers, 94(3), 491–502.CrossRefGoogle Scholar
  8. Cova, T., & Conger, S. (2003). Transportation hazards. In M. Kutz (Ed.), Transportation engineer’s handbook.Google Scholar
  9. Delmelle, E., Shuping, L., & Murray, A. T. (2012). Identifying bus stop redundancy: A GIS-based spatial optimization approach. Computers, Environment and Urban Systems, 36(5), 445–455.CrossRefGoogle Scholar
  10. Densham, P., & Rushton, G. (1992). A more efficient heuristic for solving large p-median problems. Papers in Regional Science: The Journal of the RSAI, 71(3), 307–329.CrossRefGoogle Scholar
  11. Garcia, M. L. (2008). Design and evaluation of physical protection systems. Butterworth-Heinemann.Google Scholar
  12. George, R. (2008). Critical infrastructure protection. International Journal of Critical Infrastructure Protection, 1(1), 4–5.CrossRefGoogle Scholar
  13. Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford: Oxford University Press.Google Scholar
  14. Grubesic, Tony H., & Murray, Alan T. (2006). Vital nodes, interconnected infrastructures, and the geographies of network survivability. Annals of the Association of American Geographers, 96(1), 64–83.CrossRefGoogle Scholar
  15. Hilbe, J. (2007). Negative binomial regression. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Israeli, E., & Wood, K. (2002). Shortest path network interdiction. Networks, 40(2), 97–111.CrossRefGoogle Scholar
  17. Lim, C., & Smith, J. C. (2007). Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Transactions, 39(1), 15–26.CrossRefGoogle Scholar
  18. Lin, J., & Ban, Y. (2013). Complex network topology of transportation systems. Transport Reviews, 33(6), 658–685.CrossRefGoogle Scholar
  19. Matisziw, T., Murray, A., & Grubesic, T. (2007). Bounding network interdiction vulnerability through cut-set identification. In A. Murray & T. Grubesic (Eds.), Critical infrastructure: Reliability and vulnerability (pp. 243–255). Heidelberg: Springer.Google Scholar
  20. Meyer, B. C., Lescot, J.-M., & Laplana, R. (2009). Comparison of two spatial optimization techniques: A framework to solve multiobjective land use distribution problems. Environmental Management, 43(2), 264–281.CrossRefGoogle Scholar
  21. Miller, H. J., & Wentz, E. A. (2003). Representation and spatial analysis in geographic information systems. Annals of the Association of American Geographers, 93(3), 574–594.CrossRefGoogle Scholar
  22. Murray, A. T. (2013). An overview of network vulnerability modeling approaches. GeoJournal, 78(2), 209–221.CrossRefGoogle Scholar
  23. Murray, A., Matisziw, T., & Grubesic, T. (2007). Critical network infrastructure analysis: Interdiction and system flow. Journal of Geographical Systems, 9(2), 103–117.CrossRefGoogle Scholar
  24. Ohman, K., & Eriksson, L. O. (2002). Allowing for spatial consideration in long-term forest planning by linking linear programming with simulated annealing. Forest Ecology and Management, 161(1–3), 221–230.CrossRefGoogle Scholar
  25. Przemieniecki, J. S. (2000). Mathematical methods in defense analysis. Reston, Virginia: AIAA Education Series.CrossRefGoogle Scholar
  26. Reese, J. (2006). Solution methods for the p-median problem: An annotated bibliography. Networks, 48(3), 125–142.CrossRefGoogle Scholar
  27. Salmeron, J., Wood, R. K., & Baldick, R. (2004). Analysis of electric grid security under terrorist threat. IEEE Transactions on Power Systems, 19(2), 105–912.Google Scholar
  28. Snediker, D. E., Murray, A. T., & Matisziw, T. C. (2008). Decision support for network disruption mitigation. Decision Support Systems, 44(4), 954–969.CrossRefGoogle Scholar
  29. Tong, D., & Murray, A. (2012). Spatial optimization in geography. Annals of the Association of American Geographers, 102(6), 1290–1309.CrossRefGoogle Scholar
  30. Wood, K. (1993). Deterministic network interdiction. Mathematical and Computer Modelling, 17(2), 1–18.CrossRefGoogle Scholar
  31. Yates, J., Batta, R., & Karwan, M. (2011). Optimal placement of sensors and interception resource assessment for the protection of regional infrastructure from covert attack. Journal of Transport Security, 4(2), 145–169.Google Scholar
  32. Yates, J., & Casas, I. (2012). Role of spatial data in the protection of critical infrastructure and homeland defense. Applied Spatial Analysis and Policy, 5(1), 1–23.CrossRefGoogle Scholar
  33. Yates, J., & Lakshmanan, K. (2011). A constrained binary knapsack approximation for shortest path interdiction. Computers & Industrial Engineering, 61(4), 981–992.Google Scholar
  34. Zhang, T., Madhani, S., & van den Berg, E. (2005). Sensor on patrol (SOP): Using mobile sensors to detect potential airborn nuclear, biological and chemical attacks. In IEEE military communications conference MILCOM (pp. 2924–2929).Google Scholar
  35. Zhuang, J., & Bier, V. (2007). Balancing terrorism and natural disasters—defensive strategy with endogneous attacker effect. Operations Research, 55(5), 976–991.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Louisiana Tech UniversityRustonUSA

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