Fast Algorithms for a Class of Temporal Range Queries

  • Qingmin Shi
  • Joseph JaJa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)

Abstract

Given a set of n objects, each characterized by d attributes specified at m fixed time instances, we are interested in the problem of designing efficient indexing structures such that the following type of queries can be handled efficiently: given d value ranges and a time interval, report or count all the objects whose attributes fall within the corresponding d value ranges at each time instance lying in the specified time interval. We establish efficient data structures to handle several classes of the general problem. Our results include a linear size data structure that enables a query time of O(log n log m + f) for one-sided queries when d=1, where f is the output size. We also show that the most general problem can be solved with polylogarithmic query time using nonlinear space data structures.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agarwal, P.K., Arge, L., Erickson, J.: Indexing moving points. In: 19th ACM Symp. Principles of Database Systems, pp. 175–186 (2000)Google Scholar
  2. 2.
    Chazelle, B.: Filtering search: A new approach to query-answering. SIAM J. Computing 15(3), 703–724 (1986)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chazelle, B.: A functional approach to data structures and its use in multidimensional searching. SIAM J. Computing 17(3), 427–463 (1988)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chazelle, B.: Lower bounds for orthogonal range search I. The arithmetic model. J. ACM 37(3), 439–463 (1990)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chazelle, B.: Lower bounds for orthogonal range search I. The reporting case. J. ACM 37(2), 200–212 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Driscoll, J.R., Sarnak, N., Sleattor, D., Tarjan, R.E.: Make data structures persistent. J. of Comput. and Syst. Sci. 38, 86–124 (1989)MATHCrossRefGoogle Scholar
  7. 7.
    Fredman, M.L., Willard, D.E.: Trans-dichotomous algorithms for minimum spanning trees and shortest paths. J. Comput. and Syst. Sci. 48, 533–551 (1994)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. 16th Annual ACM Symp. Theory of Computing, pp. 135–143 (1984)Google Scholar
  9. 9.
    Gupta, P., Janardan, R., Smid, M.: Further results on generalized intersection searching problems: counting, reporting, and dynamization. J. Algorithms 19, 282–317 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM J. Computing 13(2), 338–355 (1984)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Janardan, R., Lopez, M.: Generalized intersection searching problems. International Journal of Computational Geometry & Applications 3(1), 39–69 (1993)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Lanka, S., Mays, E.: Fully persistent B + -trees. In: Proc. ACM SIGMOD Int. Conf. on Management of Data, pp. 426–435 (1991)Google Scholar
  13. 13.
    Makris, C., Tsakalidis, A.K.: Algorithms for three-dimensional dominance searching in linear space. Information Processing Letters 66(6), 277–283 (1998)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Manolopoulos, Y., Kapetanakis, G.: Overlapping B + -trees for temporal data. In: Proc. 5th Jerusalem Conf. on Information Technology, pp. 491–498 (1990)Google Scholar
  15. 15.
    McCreight, E.M.: Priority search trees. SIAM J. Computing 14(2), 257–276 (1985)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Nascimento, M.A., Silva, J.R.O.: Towards historical R-trees. In: Proc. ACM Symp. Applied Computing, pp. 235–240 (1998)Google Scholar
  17. 17.
    Saltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. In: Proc. 2000 ACM SIGMOD Int. Conf. on Management of Data, pp. 331–342 (2000)Google Scholar
  18. 18.
    Shi, Q., JaJa, J.: Fast algorithms for 3-d dominance reporting and counting. Technical Report CS-TR-4437, Institute of Advanced Computer Study (UMIACS), Unveristy of Maryland (2003) Google Scholar
  19. 19.
    Tao, Y., Papadias, D.: Efficient historical R-trees. In: Proc. 13th Int. Conf. on Scientific and Statistical Database Management, pp. 223–232 (2001)Google Scholar
  20. 20.
    Tzouramanis, T., Manolopoulos, Y., Vassilakopoulos, M.: Overlapping Linear Quadtrees: A spatio-temporal access method. In: Proc. of the 6th ACM Symp. on Advances in Geographic Information Systems (ACM-GIS), pp. 1–7 (1998)Google Scholar
  21. 21.
    Tzouramanis, T., Vassilakopoulos, M., Manolopoulos, Y.: Processing of spatiotemporal queries in image databases. In: Eder, J., Rozman, I., Welzer, T. (eds.) ADBIS 1999. LNCS, vol. 1691, pp. 85–97. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Varman, P.J., Verma, R.M.: An efficient multiversion access structure. IEEE Trans. Knowledge and Data Engineering 9(3), 391–409 (1997)CrossRefGoogle Scholar
  23. 23.
    Vuillemin, J.: A unifying look at data structures. Comm. ACM 23(4), 229–239 (1980)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Willard, D.E.: Examining computational geometry, van Emde Boas trees, and hashing from the perspective of the fusion three. SIAM J. Computing 29(3), 1030–1049 (2000)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Qingmin Shi
    • 1
  • Joseph JaJa
    • 1
  1. 1.Institute for Advanced Computer Studies, Department of Electrical and Computer EngineeringUniversity of MarylandCollege ParkUSA

Personalised recommendations