GeoInformatica

, Volume 17, Issue 4, pp 669–696 | Cite as

Decentralized querying of topological relations between regions monitored by a coordinate-free geosensor network

Article

Abstract

Geosensor networks present unique resource constraints to spatial computation, including limited battery power, communication constraints, and frequently a lack of coordinate positioning systems. As a result, there is a need for new algorithms that can efficiently satisfy basic spatial queries within those resource constraints. This paper explores the design and evaluation of a family of new algorithms for determining the topological relations between regions monitored by such a resource-constrained geosensor network. The algorithms are based on efficient, decentralized (in-network) variants of conventional 4-intersection and intersection and difference models, with in-network data aggregation. Further, our algorithms operate without any coordinate information, making them suitable applications where a positioning system is unavailable or unreliable. While all four algorithms are shown to have overall communication complexity O(n) and optimal load balance O(1), the algorithms differ in the level of topological detail they can detect; the types of regions they can monitor; and in the constant factors for communication complexity. The paper also demonstrates the impact of finite granularity observations on the correctness of the query results. In the conclusions, we identify the need to conduct further fundamental research on the relationship between topological relations between regions and limited granularity sensor observations of those regions.

Keywords

Geosensor network Decentralized spatial computing 4-intersection model Intersection and difference model Granularity 

Notes

Acknowledgements

This work was supported under the Australian Research Council (ARC) Future Fellowship funding scheme (grant number FT0990531) and the ARC Discovery Project scheme (grant number DP120103758).

References

  1. 1.
    Bredon GE (1993) Topology and geometry. Springer, New YorkCrossRefGoogle Scholar
  2. 2.
    Clementini E, Felice PD, Califano G (1995) Composite regions in topological queries. Inf Syst 20(7):579–594CrossRefGoogle Scholar
  3. 3.
    Cohn AG, Bennett B, Gooday J, Gotts NM (1997) Qualitative spatial representation and reasoning with the region connection calculus. Geoinformatica 1:275–316. doi: 10.1023/A:1009712514511 CrossRefGoogle Scholar
  4. 4.
    Deng M, Cheng T, Chen X, Li Z (2007) Multi-level topological relations between spatial regions based upon topological invariants. Geoinformatica 11(2):239–267CrossRefGoogle Scholar
  5. 5.
    Duckham M (2013) Decentralized spatial computing: foundations of geosensor networks. Springer, BerlinCrossRefGoogle Scholar
  6. 6.
    Duckham M, Jeong MH, Li S, Renz J (2010) Decentralized querying of topological relations between regions without using localization. In: Proc. 18th SIGSPATIAL international conference on advances in geographic information systems, GIS ’10. ACM, New York, pp 414–417Google Scholar
  7. 7.
    Duckham M, Nussbaum D, Sack JR, Santoro N (2011) Efficient, decentralized computation of the topology of spatial regions. IEEE Trans Comput 60:1100–1113CrossRefGoogle Scholar
  8. 8.
    Egenhofer MJ, Fransoza RD (1991) Point-set topological spatial relations. Int J Geogr Inf Syst 5(2):161–174CrossRefGoogle Scholar
  9. 9.
    Egenhofer MJ, Herring J (1992) Categorizing binary topological relationships between regions, lines, and points in geographic databases. Tech. rep., Department of Surveying Engineering, University of Maine, Orono, MEGoogle Scholar
  10. 10.
    Egenhofer MJ, Clementini E, Di Felice P (1994) Topological relations between regions with holes. Int J Geogr Inf Syst 8(2):129–144CrossRefGoogle Scholar
  11. 11.
    Farah C, Zhong C, Worboys M, Nittel S (2008) Detecting topological change using a wireless sensor network. In: Cova T, Beard K, Goodchild M, Frank A (eds) GIScience 2008. Lecture notes in computer science, vol 5266. Springer, Berlin, pp 55–69Google Scholar
  12. 12.
    Greenwald MB, Khanna S (2004) Power-conserving computation of order-statistics over sensor networks. In: Proc. 23rd ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems (PODS). ACM, New York, pp 275–285Google Scholar
  13. 13.
    Guan LJ, Duckham M (2011) Decentralized reasoning about gradual changes of topological relationships between continuously evolving regions. In: Egenhofer MJ, Giudice NA, Moratz R, Worboys MF (eds) Conference on spatial information theory (COSIT ’11). Lecture notes in computer science, vol 6899. Springer, Berlin, pp 126–147CrossRefGoogle Scholar
  14. 14.
    Hatcher A (2005) Notes on introductory point-set topology. http://www.math.cornell.edu/%7Ehatcher/Top/TopNotes.pdf
  15. 15.
    Jiang J, Worboys M (2008) Detecting basic topological changes in sensor networks by local aggregation. In: Proc. 16th ACM international conference on advances in geographic information systems (ACMGIS). ACM, New York, pp 1–10Google Scholar
  16. 16.
    Khan A, Schneider M (2010) Topological reasoning between complex regions in databases with frequent updates. In: Proc. 18th SIGSPATIAL international conference on advances in geographic information systems, GIS ’10. ACM, New York, pp 380–389Google Scholar
  17. 17.
    Krishnamachari B, Estrin D, Wicker SB (2002) The impact of data aggregation in wireless sensor networks. In: Proc. 22nd international conference on distributed computing systems (ICDCS). IEEE, pp 575–578Google Scholar
  18. 18.
    Lian J, Chen L, abd Yunhao Liu KN, Agnew GB (2007) Gradient boundary detection for time series snapshot construction in sensor networks. IEEE Trans Parallel Distrib Syst 18(10):1462–1475CrossRefGoogle Scholar
  19. 19.
    Madden S, Franklin MJ, Hellerstein JM, Hong W (2002) TAG: a tiny aggregation service for ad-hoc sensor networks. In: Proc. 5th symposium on operating system design and implementation (OSDI), pp 131–146Google Scholar
  20. 20.
    Mandelbrot BB (1977) Fractals, form, chance and dimension. San FranciscoGoogle Scholar
  21. 21.
    Nguyen V, Parent C, Spaccapietra S (1997) Complex regions in topological queries. In: Hirtle S, Frank A (eds) Spatial information theory a theoretical basis for GIS. Lecture notes in computer science, vol 1329. Springer, Berlin, pp 175–192CrossRefGoogle Scholar
  22. 22.
    Nittel S (2009) A survey of geosensor networks: advances in dynamic environmental monitoring. Sensors 9(7):5664–5678CrossRefGoogle Scholar
  23. 23.
    Randell DA, Cui Z, Cohn AG (1992) A spatial logic based on regions and connection. In: Nebel B, Swartout W, Rich C (eds) In: Proc. 3rd International conference on knowledge representation and reasoning, pp 156–176Google Scholar
  24. 24.
    Rosenfeld A (1979) Digital topology. Am Math Mon 86(8):621–630CrossRefGoogle Scholar
  25. 25.
    Rosso R, Bacchi B, Barbera PL (1991) Fractal relation of mainstream length to catchment area in river networks. Water Resour Res 27(4):381–387CrossRefGoogle Scholar
  26. 26.
    Sadeq M, Duckham M (2008) Effect of neighborhood on in-network processing in sensor networks. In: Cova T, Beard K, Goodchild M, Frank A (eds) GIScience 2008. Lecture notes in computer science, vol 5266. Springer, Berlin, pp 133–150Google Scholar
  27. 27.
    Sadeq MJ, Duckham M (2009) Decentralized area computation for spatial regions. In: Proc. 17th ACM SIGSPATIAL international conference on advances in geographic information systems, pp 432–435Google Scholar
  28. 28.
    Santoro N (2007) Design and analysis of distributed algorithms. Wiley, New JerseyGoogle Scholar
  29. 29.
    Sarkar R, Zhu X, Gao J, Guibas LJ, Mitchell JSB (2008) Iso-contour queries and gradient descent with guaranteed delivery in sensor networks. In: Proc. 27th IEEE conference on computer communications (INFOCOM), pp 960–967Google Scholar
  30. 30.
    Schneider M, Behr T (2006) Topological relationships between complex spatial objects. ACM Trans Database Syst 31(1):39–81CrossRefGoogle Scholar
  31. 31.
    Sharifzadeh M, Shahabi C (2005) Utilizing Voronoi cells of location data streams for accurate computation of aggregate functions in sensor networks. Geoinformatica 10(1):9–36CrossRefGoogle Scholar
  32. 32.
    Shen G (2002) Fractal dimension and fractal growth of urbanized areas. Int J Geogr Inf Sci 16(5):419–437CrossRefGoogle Scholar
  33. 33.
    Shi M, Winter S (2010) Detecting change in snapshot sequences. In: Fabrikant S, Reichenbacher T, van Kreveld M, Schlieder C (eds) Geographic information science. Lecture notes in computer science, vol 6292. Springer, Berlin, pp 219–233CrossRefGoogle Scholar
  34. 34.
    Shrivastava N, Buragohain C, Agrawal D, Suri S (2004) Medians and beyond: new aggregation techniques for sensor networks. In: Proc. 2nd international conference on embedded networked sensor systems (SenSys). ACM, New York, pp 239–249CrossRefGoogle Scholar
  35. 35.
    Skraba P, Fang Q, Nguyen A, Guibas L (2006) Sweeps over wireless sensor networks. In: Proc. 5th international conference on information processing in sensor networks (IPSN), pp 143–151Google Scholar
  36. 36.
    Tarboton DG, Bras RL, Rodriguez-Iturbe I (1988) The fractal nature of river networks. Water Resour Res 24(8):1317–1322CrossRefGoogle Scholar
  37. 37.
    Wilensky U (1999) Netlogo. http://ccl.northwestern.edu/netlogo/
  38. 38.
    Winter S (1995) Topological relations between discrete regions. In: Egenhofer M, Herring J (eds) Advances in spatial databases. Lecture notes in computer science, vol 951. Springer, Berlin, pp 310–327CrossRefGoogle Scholar
  39. 39.
    Worboys MF, Duckham M (2006) Monitoring qualitative spatiotemporal change for geosensor networks. Int J Geogr Inf Sci 20(10):1087–1108CrossRefGoogle Scholar
  40. 40.
    Zheng R, Barton R (2007) Toward optimal data aggregation in random wireless sensor networks. In: Proc. 26th IEEE international conference on computer communications (INFOCOM). IEEE, Washington, DC, pp 249–257Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Infrastructure EngineeringUniversity of MelbourneMelbourneAustralia

Personalised recommendations