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Moving Objects: Logical Relationships and Queries

  • Jianwen Su
  • Haiyan Xu
  • Oscar H. Ibarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2121)

Abstract

In moving object databases, object locations in some multidimensional space depend on time. Previous work focuses mainly on moving object modeling (e.g., using ADTs, temporal logics) and ad hoc query optimization. In this paper we investigate logical properties of moving objects in connection with queries over such objects using tools from differential geometry. In an abstract model, object locations can be described as vectors of continuous functions of time. Using this conceptual model, we examine the logical relationships between moving objects, and between moving objects and (stationary) spatial objects in the database. We characterize these relationships in terms of position, velocity, and acceleration. We show that these fundamental relationships can be used to describe natural queries involving time instants and intervals. Based on this foundation, we develop a concrete data model for moving objects which is an extension of linear constraint databases. We also present a preliminary version of a logical query language for moving object databases.

Keywords

Time Instant Linear Constraint Query Language Spatial Database Relation Schema 
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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References

  1. [AAE00]
    P. Agarwal, L. Arge, and J. Erickson. Indexing moving points. In Proc. ACM Symp. on Principles of Database Systems, 2000.Google Scholar
  2. [AHV95]
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.Google Scholar
  3. [BBC98]
    A. Belussi, E. Bertino, and B. Catania. An extended algebra for constraint databases. IEEE Trans. on Knowledge and Data Engineering, 10(5):686–705, 1998.CrossRefGoogle Scholar
  4. [BKR86]
    M. Ben-Or, D. Kozen, and J. Reif. The complexity of elementary algebra and geometry. Journal of Computer and System Sciences, 32(2):251–264, April 1986.Google Scholar
  5. [Col75]
    G. E. Collins. Quantifier elimination for real closed fields by cylindric decompositions. In Proc. 2nd GI Conf. Automata Theory and Formal Languages, volume 35 of Lecture Notes in Computer Science, pages 134–83. Springer-Verlag, 1975.Google Scholar
  6. [EF91]
    M. J. Egenhofer and R. Franzosa. Point-set topological spatial relations. Int. Journal of Geo. Info. Systems, 5(2):161–174, 1991.CrossRefGoogle Scholar
  7. [Ege91]
    M. J. Egenhofer. Reasonning about binary topological relations. In Proc. Symp. on Large Spatial Databases, 1991.Google Scholar
  8. [EGSV99]
    M. Erwig, R. H. Guting, M. Schneider, and M. Vazirgiannis. Spatiotemporal data types: an approach to modeling and querying moving objects in databases. GeoInformatica, 3(3):269–296, 1999.CrossRefGoogle Scholar
  9. [Eme90]
    E. A. Emerson. Temporal and modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 7, pages 995–1072. North Holland, 1990.Google Scholar
  10. [FGNS00]
    L. Forlizzi, R. H. Guting, E. Nardelli, and M. Schneider. A data model and data structures for moving objects databases. In Proc. ACM SIGMOD Int. Conf. on Management of Data, 2000.Google Scholar
  11. [GBE+00]
    R. H. Güting, M. H. Böhlen, M. Erwig, S. Jensen, N. A. Lorentzos, M. Schneider, and M. Varirgiannis. A foundation for representing and querying moving objects. ACM Transactions on Database Systems, 25(1), 2000. to appear.Google Scholar
  12. [Gra98]
    A. Gray. Modern Differential Geometry of Curves and Surfaces with Mathematica (Second Edition) CRC Press, 1998.Google Scholar
  13. [GRS98]
    S. Grumbach, P. Rigaux, and L. Segoufin. The DEDALE system for complex spatial queries. In Proc. ACM SIGMOD Int. Conf. on Management of Data, June 1998.Google Scholar
  14. [GS96]
    S. Grumbach and J. Su. Towards practical constraint databases. In Proc. ACM Symp. on Principles of Database Systems, 1996.Google Scholar
  15. [GS97]
    S. Grumbach and J. Su. Finitely representable databases. Journal of Computer and System Sciences, 55(2):273–298, October 1997.Google Scholar
  16. [KdB99]
    B. Kuijpers and J. Van den Bussche. On capturing first-order topological properties of planar spatial databases. In Proc. Int. Conf. on Database Theory, 1999.Google Scholar
  17. [KGT99]
    G. Kollios, D. Gunopulos, and V. J. Tsotras. On indexing mobile objects. In Proc. ACM Symp. on Principles of Database Systems, pages 261–272, 1999.Google Scholar
  18. [KKR95]
    P. Kanellakis, G. Kuper, and P. Revesz. Constraint query languages. Journal of Computer and System Sciences, 51(1):26–52, 1995.CrossRefMathSciNetGoogle Scholar
  19. [KLP00]
    G. Kuper, L. Libkin, and J. Paredarns, editors. Constraint Databases. Springer Verlag, 2000.Google Scholar
  20. [KPdB97]
    B. Kuijpers, J. Paredaens, and J. Van den Bussche. On topological elementary equivalence of spatial databases. In Proc. Int. Conf. on Database Theory, 1997.Google Scholar
  21. [KRSS98]
    G. Kuper, S. Ramaswamy, K. Shim, and J. Su. A constraint-based spatial extension to SQL. In Proc. ACM Symp. Geographical Information Systems, 1998.Google Scholar
  22. [MP77]
    R. S. Millman and G. D. Parker. Elements of Differential Geometry. Prentice-Hall, Edgewood Cliffs, NJ, 1977.zbMATHGoogle Scholar
  23. [PSV96]
    C. H. Papadimitriou, D. Suciu, and V. Vianu. Topological queries in spatial databases. In Proc. ACM Symp. on Principles of Database Systems, 1996.Google Scholar
  24. [Ren92]
    J. Renegar. On the computational complexity and geometry of the first-order theory of the reals. Journal of Symbolic Computation, 13:255–352, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  25. [SWCD97]
    A. P. Sistla, O. Wolfson, S. Chamberlain, and S. Dao. Modeling and querying moving objects. In Proc. Int. Conf. on Data Engineering, 1997.Google Scholar
  26. [Tar51]
    A. Tarski. A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley, California, 1951.zbMATHGoogle Scholar
  27. [WCD+98]
    O. Wolfson, S. Chamberlain, S. Dao, L. Jiang, and G. Mendez. Cost and imprecision in modeling the position of moving objects. In Proc. Int. Conf. on Data Engineering, Orlando, FL, 1998.Google Scholar
  28. [WCDJ97]
    O. Wolfson, S. Chamberlain, S. Dao, and L. Jiang. Location management in moving objects databases. In Proc. the Second International Workshop on Satellite-Based Information Services (WOSBIS’97), Budapest, Hungary, October 1997.Google Scholar
  29. [WJS+99]
    O. Wolfson, L. Jiang, P. Sistla, S. Chamberlain, N. Rishe, and M. Deng. Databases for tracking mobile units in real time. In Proc. Int. Conf. on Database Theory, pages 169–186, Jerusalem, Israel, 1999.Google Scholar
  30. [WXCJ98]
    O. Wolfson, B. Xu, S. Chamberlain, and L. Jiang. Moving objects databases: issues and solutions. In Proc. Int. Conf. on Statistical and Scientific Database Management, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jianwen Su
    • 1
  • Haiyan Xu
    • 1
  • Oscar H. Ibarra
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

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