Practical Approaches to Partially Guarding a Polyhedral Terrain

  • Frank Kammer
  • Maarten Löffler
  • Paul Mutser
  • Frank Staals
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8728)


We study the problem of placing guard towers on a terrain such that the terrain can be seen from at least one tower. This problem is important in many applications, and has an extensive history in the literature (known as, e.g., multiple observer siting). In this paper, we consider the problem on polyhedral terrains, and we allow the guards to see only a fixed fraction of the terrain, rather than everything. We experimentally evaluate how the number of required guards relates to the fraction of the terrain that can be covered. In addition, we introduce the concept of dominated guards, which can be used to preprocess the potential guard locations and speed up the subsequent computations.


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  1. 1.
    Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Geometric approximation via coresets. In: Combinatorial and Computational Geometry, pp.1–30. University Press, MSRI (2005)Google Scholar
  2. 2.
    Alon, N., Moshkovitz, D., Safra, S.: Algorithmic construction of sets for k-restrictions. ACM Transactions on Algorithms, 153–177 (2006)Google Scholar
  3. 3.
    Aspbury, A.S., Gibson, R.M.: Long-range visibility of greater sage grouse leks: A gis-based analysis. Animal Behaviour 67(6), 1127–1132 (2004)CrossRefGoogle Scholar
  4. 4.
    Burrough, P.A., McDonnell, R., Burrough, P.A., McDonnell, R.: Principles of geographical information systems, vol. 333. Oxford University Press, Oxford (1998)Google Scholar
  5. 5.
    Camp, R.J., Sinton, D.T., Knight, R.L.: Viewsheds: A complementary management approach to buffer zones. Wildlife Society Bulletin 25(3), 612–615 (1997)Google Scholar
  6. 6.
    Catry, F.X., Rego, F.C., Santos, T., Almeida, J., Relvas, P.: Fires prevention in Portugal - using GIS to help improving early fire detection effectiveness. In: 4th Int. Wildland Fire Conf. (2007)Google Scholar
  7. 7.
    Cole, R., Sharir, M.: Visibility problems for polyhedral terrains. Journal of Symbolic Computation 7(1), 11–30 (1989)CrossRefMathSciNetGoogle Scholar
  8. 8.
    De Floriani, L., Marzano, P., Puppo, E.: Line-of-sight communication on terrain models. International Journal of Geographical Information Systems 8(4), 329–342 (1994)CrossRefGoogle Scholar
  9. 9.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity, p. 530. Springer (1999)Google Scholar
  10. 10.
    Eidenbenz, S., Stamm, C., Widmayer, P.: Positioning guards at fixed height above a terrain – an optimum inapproximability result. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 187–198. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Floriani, L.D., Magillo, P.: Algorithms for visibility computation on terrains: A survey. Environ. Plann. B 30(5), 709–728 (2003)CrossRefGoogle Scholar
  12. 12.
    Franklin, W.: Siting observers on terrain. In: Richardson, D., Oosterom, P. (eds.) Advances in Spatial Data Handling, pp. 109–120. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. WH Freeman & Co., New York (1979)zbMATHGoogle Scholar
  14. 14.
    Hurtado, F., Löffler, M., Matos, I., Sacristán, V., Saumell, M., Silveira, R.I., Staals, F.: Terrain visibility with multiple viewpoints. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) ISAAC2013. LNCS, vol. 8283, pp. 317–327. Springer, Heidelberg (2013)Google Scholar
  15. 15.
    Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9(3), 256–278 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Jones, N.L., Wright, S.G., Maidment, D.R.: Watershed delineation with triangle-based terrain models. Journal of Hydraulic Engineering 116(10), 1232–1251 (1990)CrossRefGoogle Scholar
  17. 17.
    Katz, M.J., Overmars, M.H., Sharir, M.: Efficient hidden surface removal for objects with small union size. Computational Geometry 2(4), 223–234 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Kim, Y.H., Rana, S., Wise, S.: Exploring multiple viewshed analysis using terrain features and optimisation techniques. Computers & Geosciences 30, 1019–1032 (2004)CrossRefGoogle Scholar
  19. 19.
    van Kreveld, M.: Digital elevation models and tin algorithms. In: van Kreveld, M., Roos, T., Nievergelt, J., Widmayer, P. (eds.) CISM School 1996. LNCS, vol. 1340, pp. 37–78. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  20. 20.
    Lv, P., Zhang, J.-f., Lu, M.: An optimal method for multiple observers sitting on terrain based on improved simulated annealing techniques. In: Ali, M., Dapoigny, R. (eds.) IEA/AIE 2006. LNCS (LNAI), vol. 4031, pp. 373–382. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Magalhaes, S.V.G., Andrade, M.V.A., Franklin, W.R.: An optimization heuristic for siting observers in huge terrains stored in external memory. In: 2010 10th International Conference on Hybrid Intelligent Systems (HIS), August 2010, pp. 135–140 (2010)Google Scholar
  22. 22.
    Silfer, A.T., Kinn, G.J., Hassett, J.M.: A geographic information system utilizing the triangulated irregular network as a basis for hydrologic modeling. In: Proc. Auto-Carto., vol. 8, pp. 129–136 (1987)Google Scholar
  23. 23.
    Silveira, R.I.: Optimization of polyhedral terrains. ASCI Disseratation Series (178) (2009)Google Scholar
  24. 24.
    Stephen, B.K., Wicker, S.B.: Experimental analysis of local search algorithms for optimal base station location (2000)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Frank Kammer
    • 1
  • Maarten Löffler
    • 2
  • Paul Mutser
    • 2
  • Frank Staals
    • 2
  1. 1.Institut für InformatikUniversität AugsburgAugsburgGermany
  2. 2.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands

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