An Efficient Indexing Scheme for Multi-dimensional Moving Objects

  • Khaled Elbassioni
  • Amr Elmasry
  • Ibrahim Kamel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2572)


We consider the problem of indexing a set of objects moving in d-dimensional space along linear trajectories. A simple disk-based indexing scheme is proposed to efficiently answer queries of the form: report all objects that will pass between two given points within a specified time interval. Our scheme is based on mapping the objects to a dual space, where queries about moving objects translate into polyhedral queries concerning their speeds and initial locations.We then present a simple method for answering such polyhedral queries, based on partitioning the space into disjoint regions and using a B-tree to index the points in each region. By appropriately selecting the boundaries of each region, we can guarantee an average search time that almost matches a known lower bound for the problem. Specifically, for a fixed d, if the coordinates of a given set of N points are statistically independent, the proposed technique answers polyhedral queries, on the average, in O((N/B)1-1/d .(logB N)1 /d +K/B) I/O’s using O(N/B) space, where B is the block size, and K is the number of reported points. Our approach is novel in that, while it provides a theoretical upper bound on the average query time, it avoids the use of complicated data structures, making it an effective candidate for practical applications.


Index Structure Range Query Query Time Indexing Scheme Partition Tree 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. K. Agarwal, L. Arge and J. Erickson, Indexing Moving points. In Proc. 19th ACM PODS, pp. 175–186, 2000.Google Scholar
  2. 2.
    P. K. Agarwal, L. Arge, J. Erickson, P. Franciosa and J. S. Vitter, Efficient Searching with Linear Constraints. In Proc. 17th ACM PODS, pp. 169–178, 1998.Google Scholar
  3. 3.
    R. Alonso and H. F. Korth, Database System Issues in Nomadic Computing. In Proc. ACM-SIGMOD International Conference on Management of Data, pp. 388–392, 1993.Google Scholar
  4. 4.
    A. Aggarwal and J. S. Vitter, The Input/Output Complexity of Sorting and Related Problems. In Communications of the ACM, 31(9):1116–1127, 1988.CrossRefMathSciNetGoogle Scholar
  5. 5.
    N. Beckmann, H.-P. Kriegel, R. Schneider and B. Seeger, The R.-tree: An Efficient and Robust Access Method for Points and Rectangles. In Proc. ACM-SIGMOD, pp. 322–331, 1990.Google Scholar
  6. 6.
    M. Cai, D. Keshwani and P. Z. Revesz, Parametric rectangles: A model for querying and animating spatiotemporal databases. In Proc. 7th International Conference on Extending Database Technology, LNCS 1777, pp. 430–444. Springer, 2000.Google Scholar
  7. 7.
    S. Chamberlain, Model-based battle command: A paradigm whose time has come. In Proc. 1st International Symposium on Command and Control Research and Technology, pp. 31–38, 1995.Google Scholar
  8. 8.
    B. Chazelle and B. Rosenberg, Lower Bounds on the Complexity of Simplex Range Reporting on a Pointer Machine. In Proc. 19th International Colloquium on Automata, Languages and Programming, LNCS, Vol. 693, 1992.Google Scholar
  9. 9.
    K. Elbassioni, A. Elmasry and I. Kamel, Efficient Answering of Polyhedral Queries in Rd using BBS-trees. In Proc. 14th Canadian Conference on Computational Geometry (CCCG 2002), pp. 54–57, 2002.Google Scholar
  10. 10.
    J. Goldstein, R. Ramakrishnan, U. Shaft and J. B. Yu, Processing Queries by Linear Constraints. In Proc. 16th ACM PODS, pp. 257–267, 1997.Google Scholar
  11. 11.
    A. Guttman, R-trees: A Dynamic Index Structure for Spatial Searching. In Proc. ACM-SIGMOD, pp. 47–57, 1984.Google Scholar
  12. 12.
    G. Kollios, D. Gunopulos and V. Tsotras, On Indexing Mobile Objects. In Proc. 18th ACM PODS, pp. 261–272, 1999.Google Scholar
  13. 13.
    H. V. Jagadish, On Indexing Line Segments. In Proc. 16th VLDB Conference, pp. 614–625, 1990.Google Scholar
  14. 14.
    I. Kamel and C. Faloutsos, On Packing R-trees. In Proc. Second International Conference on Information and Knowledge Management, 1993.Google Scholar
  15. 15.
    J. Matoušek, Efficient Partition Trees. Disc. and Computational Geometry, 8 (1992), pp. 432–448.Google Scholar
  16. 16.
    S. Šaltenis, C. S. Jensen, S. T. Leutenegger, and M. A. Lopez, Indexing the Positions of Continuously Moving Objects. In Proc. ACM-SIGMOD, pp. 331–342, 2000.Google Scholar
  17. 17.
    A. Schrijver. Theory of Linear and Integer Programming, Wiley-Interscience, 1986.Google Scholar
  18. 18.
    A. P. Sistla, O. Wolfson, S. Chamberlain and S. Dao, Modeling and Querying Moving Objects. In Proc. 13th IEEE ICDE Conference, pp. 422–432, April 1997.Google Scholar
  19. 19.
    J. Tayeb, O. Ulusoy and O. Wolfson, A quadtree-Based Dynamic Attribute Indexing Method. The Computer Journal, 41(3):185–200, 1998.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Khaled Elbassioni
    • 1
  • Amr Elmasry
    • 1
  • Ibrahim Kamel
    • 2
  1. 1.Computer Science DepartmentAlexandria UniversityEgypt
  2. 2.College of Information SystemsZayed UniversityUnited Arab Emirates

Personalised recommendations