Decentralized Reasoning about Gradual Changes of Topological Relationships between Continuously Evolving Regions

  • Lin-Jie Guan
  • Matt Duckham
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6899)


A key challenge facing many applications of new geosensor networks technology is to derive meaningful spatial knowledge from low-level sensed data. This paper presents a formal model for representing and computing topological relationship changes between continuously evolving regions monitored by a geosensor network. The definition of “continuity” is used to constrain region evolution and enables the local detection of node state transitions in the network. The model provides a computational framework for the detection of global high-level qualitative relationship changes from local low-level quantitative sensor measurements. In this paper, an efficient decentralized algorithm is also designed and implemented to detect relationship changes and its computational efficiency is evaluated experimentally using simulation.


Sensor Node Wireless Sensor Network Node State Gradual Change Spatial Region 
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.


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  1. 1.
    Stefanidis, A., Nittel, S.: GeoSensor Networks. CRC Press, Boca Raton (2005)Google Scholar
  2. 2.
    Egenhofer, M., Franzosa, R.: Point-set topological spatial relations. International Journal of Geographical Information Systems 5, 161–174 (1991)CrossRefGoogle Scholar
  3. 3.
    Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: 3rd International Conference on Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufmann, San Francisco (1992)Google Scholar
  4. 4.
    Clementini, E., Felice, P.D., van Oosterom, P.: A small set of formal topological relationships suitable for end-user interaction. In: Proceedings of the Third International Sym. on Advances in Spatial Databases, pp. 277–295 (1993)Google Scholar
  5. 5.
    Zhao, F., Guibas, L.J.: Wireless Sensor Networks: An Information Processing Approach. Elsevier, Amsterdam (2004)Google Scholar
  6. 6.
    Estrin, D., Govindan, R., Heidemann, J., Kumar, S.: Next century challenges: scalable coordination in sensor networks. In: Proceedings of the 5th International Conference on Mobile Computing and Networking, pp. 263–270. ACM, New York (1999)Google Scholar
  7. 7.
    Madden, S., Franklin, M., Hellerstein, J., Hong, W.: TAG: a tiny aggregation service for ad-hoc sensor networks. In: 5th Annual Symposium on Operating Systems Design and Implementation (OSDI), pp. 1–16 (2002)Google Scholar
  8. 8.
    Hellerstein, J.M., Hong, C.-M., Madden, S., Stanek, K.: Beyond average: Toward sophisticated sensing with queries. In: Zhao, F., Guibas, L.J. (eds.) IPSN 2003. LNCS, vol. 2634, pp. 63–79. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Klippel, A., Li, R.: The endpoint hypothesis: A topological-cognitive assessment of geographic scale movement patterns. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds.) COSIT 2009. LNCS, vol. 5756, pp. 177–194. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Guibas, L.J.: Sensing, tracking and reasoning with relations. IEEE Signal Processing Magazine 19(2), 73–85 (2002)CrossRefGoogle Scholar
  11. 11.
    Worboys, M.F., Duckham, M.: Monitoring qualitative spatiotemporal change for geosensor networks. International Journal of Geographic Information Science 20(10), 1087–1108 (2006)CrossRefGoogle Scholar
  12. 12.
    Farah, C., Zhong, C., Worboys, M., Nittel, S.: Detecting topological change using a wireless sensor network. In: Cova, T.J., Miller, H.J., Beard, K., Frank, A.U., Goodchild, M.F. (eds.) GIScience 2008. LNCS, vol. 5266, pp. 55–69. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Jiang, J., Worboys, M.: Event-based topology for dynamic planar areal objects. International Journal of Geographical Information Science 23(1), 33–60 (2009)CrossRefGoogle Scholar
  14. 14.
    Sadeq, M.J.: In network detection of topological change of region with a wireless sensor network. PhD thesis, The University of Melbourne (2009)Google Scholar
  15. 15.
    Jiang, J., Worboys, M., Nittel, S.: Qualitative change detection using sensor networks based on connectivity information. GeoInformatica, 1–24 (2009) (accepted)Google Scholar
  16. 16.
    Shi, M., Winter, S.: Detecting change in snapshot sequences. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) GIScience 2010. LNCS, vol. 6292, pp. 219–233. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Liu, H., Schneider, M.: Tracking continuous topology changes of complex moving regions. In: 26th Annual ACM Symp. on Applied Computing, ACM SAC (2011)Google Scholar
  18. 18.
    Jin, G., Nittel, S.: Efficient tracking of 2D objects with spatiotemporal properties in wireless sensor networks. Distributed and Parallel Databases 29(1), 3–30 (2011)CrossRefGoogle Scholar
  19. 19.
    Duckham, M., Nussbaum, D., Sack, J.R., Santoro, N.: Efficient, decentralized computation of the topology of spatial regions. IEEE Transactions on Computers 60 (2011), doi:10.1109/TC.2010.177 (in press)Google Scholar
  20. 20.
    Guan, L.J., Duckham, M.: Decentralized computing of topological relationships between heterogeneous regions. In: Lees, B., Laffan, S. (eds.) Proc. 10th International Conference on GeoComputation, Sydney, Australia (2009)Google Scholar
  21. 21.
    Duckham, M., Jeong, M.H., Li, S., Renz, J.: Decentralized querying of topological relations between regions without using localization. In: Agrawal, A.A.D., Mokbel, M., Zhang, P. (eds.) Proc. 18th ACM SIGSPATIAL GIS, pp. 414–417. ACM, New York (2010)CrossRefGoogle Scholar
  22. 22.
    Duckham, M., Stell, J., Vasardani, M., Worboys, M.: Qualitative change to 3-valued regions. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) GIScience 2010. LNCS, vol. 6292, pp. 249–263. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Egenhofer, M., Sharma, g., Mark, D.: A critical comparison of the 4-intersection and 9-intersection models for spatial relations: Formal analysis. In: McMaster, R., Armstrong, M. (eds.) Autocarto 11, pp. 1–11 (1993)Google Scholar
  24. 24.
    Egenhofer, M.J., Franzosa, R.D.: On the equivalence of topological relations. International Journal of Geographical Information Systems 9(2), 133–152 (1995)CrossRefGoogle Scholar
  25. 25.
    Rosenfeld, A.: Digital topology. The American Mathematical Monthly 86(8), 621–630 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vision Graph. Image Process. 48(3), 357–393 71400 (1989)Google Scholar
  27. 27.
    Egenhofer, M.J., Sharma, J.: Topological relations between regions in R 2 and Z 2. In: Abel, D., Ooi, B.C. (eds.) SSD 1993. LNCS, vol. 692, pp. 316–336. Springer, Heidelberg (1993)Google Scholar
  28. 28.
    Winter, S.: Topological relations between discrete regions. In: Egenhofer, M., Herring, J. (eds.) SSD 1995. LNCS, vol. 951, pp. 310–327. Springer, Heidelberg (1995)Google Scholar
  29. 29.
    Galton, A.: Continuous change in spatial regions. In: Spatial Information Theory A Theoretical Basis for GIS, pp. 1–13. Springer, Berlin (1997)CrossRefGoogle Scholar
  30. 30.
    Galton, A.: Continuous motion in discrete space. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference, pp. 26–37. Morgan Kaufmann Publishers, San Francisco (2000)Google Scholar
  31. 31.
    Egenhofer, M.: The family of conceptual neighborhood graphs for region-region relations. In: Fabrikant, S., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) GIScience 2010. LNCS, vol. 6292, pp. 42–55. Springer, Heidelberg (2010)Google Scholar
  32. 32.
    Egenhofer, M., Al-Taha, K.: Reasoning about gradual changes of topological relationships. In: Frank, A., Campari, I., Formentini, U. (eds.) GIS 1992. LNCS, vol. 639, pp. 196–219. Springer, Heidelberg (1992)Google Scholar
  33. 33.
    Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley Series on Parallel and Distributed Computing. Wiley-Interscience, Hoboken (2006)CrossRefGoogle Scholar
  34. 34.
    Mandelbrot, B.: Fractals, Form, Chance and Dimension. Freeman, San Francisco (1977)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lin-Jie Guan
    • 1
  • Matt Duckham
    • 1
  1. 1.Department of Infrastructure EngineeringThe University of MelbourneAustralia

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