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Distributed and Parallel Databases

, Volume 17, Issue 3, pp 215–249 | Cite as

An Indexing Method for Answering Queries on Moving Objects

  • Khaled Elbassioni
  • Amr Elmasry
  • Ibrahim Kamel
Article

Abstract

We consider the problem of indexing a set of objects moving in d-dimensional spaces along linear trajectories. A simple external-memory indexing scheme is proposed to efficiently answer general range queries. The following are examples of the queries that can be answered by the proposed method: report all moving objects that will (i) pass between two given points within a specified time interval; (ii) become within a given distance from some or all of a given set of other moving objects. Our scheme is based on mapping the objects to a dual space, where queries about moving objects are transformed 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 guarantee an average search time that 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⋅(log B 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. The proposed index is also dynamic in the sense that it allows object insertion and deletion in an amortized update cost of log B (N) I/O's. Experimental results are presented to show the superiority of the proposed index over other methods based on R-trees.

Keywords

B+-trees indexing mobile objects mobile database management query processing 

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References

  1. 1.
    P.K. Agarwal, L. Arge, and J. Erickson, “Indexing moving points,” in 19th ACM-PODS Symposium on Principles of Database Systems, 2000, pp. 175–186.Google Scholar
  2. 2.
    P.K. Agarwal, L. Arge, J. Erickson, P. Franciosa, and J.S. Vitter, “Efficient searching with linear constraints,” 17th ACM-PODS Symposium on Principles of Database Systems, 1998, pp. 169–178.Google Scholar
  3. 3.
    R. Alonso and H.F. Korth, “Database system issues in nomadic computing,” in ACM-SIGMOD International Conference on Management of Data, 1993, pp. 388–392.Google Scholar
  4. 4.
    A. Aggarwal and J.S. Vitter, “The input/output complexity of sorting and related problems,” Communications of the ACM, vol. 31, no. 9, pp. 1116–1127, 1988.CrossRefGoogle Scholar
  5. 5.
    ArcView GIS, ArcView Tracking Analyst, 1998.Google Scholar
  6. 6.
    N. Beckmann, H.P. Kriegel, R. Schneider, and B. Seeger, “The R*-tree: An efficient and robust access method for points and rectangles,” in ACM-SIGMOD International Conference on Management of Data, 1990, pp. 322–331.Google Scholar
  7. 7.
    B. Chazelle and B. Rosenberg, “Lower bounds on the complexity of simplex range reporting on a pointer machine,” in 19th ICALP International Colloquium on Automata, Languages and Programming, LNCS, vol. 693, 1992, pp. 439–449.Google Scholar
  8. 8.
    K. Elbassioni, A. Elmasry, and I. Kamel, “Efficient answering of polyhedral queries in ℝd using BBS-trees,” in 14th CCCG Canadian Conference on Computational Geometry, 2002, pp. 54–57.Google Scholar
  9. 9.
    K. Elbassioni, A. Elmasry, and I. Kamel, “An efficient indexing scheme for multi-dimensional moving objects,” in 9th ICDT International Conference on Database Theory, LNCS 2572, 2003, pp. 425–439.Google Scholar
  10. 10.
    V. Gaede and O. Gunther, “Multidimensional access methods,” ACM Computing Serveys, vol. 30, no. 2, pp. 170–231, 1998.CrossRefGoogle Scholar
  11. 11.
    J. Goldstein, R. Ramakrishnan, U. Shaft, and J.B. Yu, “Processing queries by linear constraints,” in 16th ACM-PODS Symposium on Principles of Database Systems, 1997, pp. 257–267.Google Scholar
  12. 12.
    A. Guttman, “R-trees: A dynamic index structure for spatial searching,” in ACM-SIGMOD International Conference on Management of Data, 1984, pp. 47–57.Google Scholar
  13. 13.
    G. Kollios, D. Gunopulos, and V. Tsotras, “On Indexing Mobile Objects.” in 18th ACM-PODS Symposium on Principles of Databases Systems, 1999, pp. 261–272.Google Scholar
  14. 14.
    H.V. Jagadish, “On Indexing Line Segments,” in 16th VLDB International Conference on Very Large Data Bases, 1990, pp. 614–625.Google Scholar
  15. 15.
    I. Kamel and C. Faloutsos, “On packing R-trees,” in 2nd International Conference on Information and Knowledge Management, 1993, pp. 490–499.Google Scholar
  16. 16.
    V. Kouramajian, I. Kamel, R. Elmasri, and S. Waheed, “The time index+: An incremental access structure for temporal databases,” in 3rd International Conference on Information and Knowledge Management, 1994, pp. 296–303.Google Scholar
  17. 17.
    J. Matoušek, “Efficient partition trees,” Discrete and Computational Geometry, vol. 8, pp. 315–334, 1992.Google Scholar
  18. 18.
    S. Saltenis, C.S. Jensen, S.T. Leutenegger, and M.A. Lopez, “Indexing the positions of continuously moving objects,” in Proc. ACM-SIGMOD International Conference on Management of Data, 2000, pp. 331–342.Google Scholar
  19. 19.
    B. Salzberg and V.J. Tsotras, “A comparison of access methods for time evolving data,” ACM Computing Surveys, vol. 31, no. 2, pp. 158–221, 1999.CrossRefGoogle Scholar
  20. 20.
    A. Schrijver, Theory of Linear and Integer Programming, 1986.Google Scholar
  21. 21.
    J. Tayeb, O. Ulusoy, and O. Wolfson, “A quadtree-based dynamic attribute indexing method,” The Computer Journal, vol. 41, no. 3, pp. 185–200, 1998.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Computer Science DepartmentAlexandria UniversityAlexandriaEgypt
  3. 3.College of Information SystemsZayed UniversityUnited Arab Emirates

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