Advertisement

Validity Information Retrieval for Spatio-Temporal Queries: Theoretical Performance Bounds

  • Yufei Tao
  • Nikos Mamoulis
  • Dimitris Papadias
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2750)

Abstract

The results of traditional spatial queries (i.e., range search, nearest neighbor, etc.) are usually meaningless in spatio-temporal applications, because they will be invalidated by the movements of query and/or data objects. In practice, a query result R should be accompanied with validity information specifying (i) the (future) time T that R will expire, and (ii) the change C of R at time T (so that R can be updated incrementally). Although several algorithms have been proposed for this problem, their worst-case performance is the same as that of sequential scan. This paper presents the first theoretical study on validity queries, and develops indexes and algorithms with attractive I/O complexities. Our discussion covers numerous important variations of the problem and different query/object mobility combinations. The solutions involve a set of non-trivial reductions that reveal the problem characteristics and permit the deployment of existing structures.

Keywords

Voronoi Diagram Near Neighbor Query Time Spatial Query 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A94]
    Arge, L.: The Buffer Tree: A New Technique for Optimal I/O Algorithms. In: WADS (1994)Google Scholar
  2. [AAE+00]
    Arge, L.: The Buffer Tree: A New Technique for Optimal I/O Algorithms. In: WADS (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [AAE00]
    Agarwal, P., Arge, L., Erickson, J.: Indexing Moving Points. In: ACM PODS (2000)Google Scholar
  4. [AAV01]
    Agarwal, P., Arge, L., Vahrenhold, J.: A Time Responsive Indexing Scheme for Moving Points. In: Workshop on Algorithms and Data Structures (2001)Google Scholar
  5. [ADT03]
    Arge, L., Danner, A., Teh, S.: I/O Efficient Point Location Using Persistent B-Trees. In: ALENEX (2003)Google Scholar
  6. [ASV99]
    Arge, L., Samoladas, V., Vitter, J.: On Two-Dimensional Indexability and Optimal Range Search Index. In: ACM PODS (1999)Google Scholar
  7. [BGH97]
    Basch, J., Guibas, L., Hershberger, J.: Data Structures for Mobile Data. In: ACM SODA (1997)Google Scholar
  8. [BGO+96]
    Becker, B., Gschwind, S., Ohler, T., Seeger, B., Widmayer, P.: An Asymptotically Optimal Multiversion B-trees. VLDB Journal 5(4), 264–275 (1996)CrossRefGoogle Scholar
  9. [BJKS02]
    Benetis, R., Jensen, C., Karciauskas, G., Saltenis, S.: Nearest Neighbor and Reverse Nearest Neighbor Queries for Moving Objects. In: IDEAS (2002)Google Scholar
  10. [BKOS97]
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  11. [BKSS90]
    Arge, L.: The Buffer Tree: A New Technique for Optimal I/O Algorithms. In: WADS (1994)Google Scholar
  12. [C88]
    Chazelle, B.: An algorithm for segment-dragging and its implementation. Algorithmica 3, 221–305 (1988)CrossRefGoogle Scholar
  13. [CGR95]
    Callahan, P., Goodrich, G., Ramaiyer, K.: Topology B-Trees and Their Applications. In: Workshop on Algorithms and Data Structures (1995)Google Scholar
  14. [GBE+00]
    Guting, R., Böhlen, M., Erwig, M., Jensen, C., Lorentzos, N., Schneider, M., Vazirgiannis, M.: A Foundation for Representing and Querying Moving Objects. In: ACM TODS, vol. 25(1), pp. 1–42 (2000)Google Scholar
  15. [GI99]
    Grossi, R., Italiano, G.: Efficient Splitting and Merging Algorithms for Order Decomposable Problems. Information and Computation 154(1), 1–33 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  16. [GLM00]
    Govindarajan, S., Lukovszki, T., Maheshwari, A., Zeh, N.: I/O-Efficient Well-Separated Pair Decomposition and Its Applications. In: Annual European Symposium on Algorithms (2000)Google Scholar
  17. [GTVV93]
    Goodrich, M., Tsay, J., Vengroff, D., Vitter, J.: External Memory Com putational Geometry. In: IEEE FOCS (1993)Google Scholar
  18. [HKP97]
    Hellerstein, J., Koutsoupias, E., Papadimitriou, C.: On the Analysis of Indexing Schemes. In: ACM PODS (1997)Google Scholar
  19. [IKO87]
    Icking, C., Klein, R., Ottmann, T.: Priority Search Trees in Secondary Memory. In: GTCCS (1987)Google Scholar
  20. [KGT99a]
    Kollios, G., Gunopulos, D., Tsotras, V.: On Indexing Mobile Objects. In: ACM PODS (1999)Google Scholar
  21. [KGT99b]
    Kollios, G., Gunopulos, D., Tsotras, V.: Nearest Neighbor Queries in Mobile Environment. In: Böhlen, M.H., Jensen, C.S., Scholl, M.O. (eds.) STDBM 1999. LNCS, vol. 1678, p. 119. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. [KRVV96]
    Kanellakis, P., Ramaswamy, S., Vengroff, D., Vitter, J.: Indexing for Data Models with Constraints and Classes. Journal of Computer and System Sciences 52(3), 589–612 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  23. [KS99]
    Kanth, K., Singh, A.: Optimal dynamic range searching in non-replicating index structures. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 257–276. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  24. [RS94]
    Ramaswamy, S., Subramanian, S.: Path Caching: A Technique for Optimal External Searching. In: ACM PODS (1994)Google Scholar
  25. [SJLL00]
    Saltenis, S., Jensen, C., Leutenegger, S., Lopez, M.: Indexing the Posi tions of Continuously Moving Objects. In: ACM SIGMOD (2000)Google Scholar
  26. [SR01]
    Song, Z., Roussopoulos, N.: K-Nearest Neighbor Search for Moving Query Point. In: Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J. (eds.) SSTD 2001. LNCS, vol. 2121, p. 79. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  27. [SR95]
    Subramanian, S., Ramaswamy, S.: The P-Range Tree: A New Data Structure for Range Searching in Secondary Memory. In: ACM SODA (1995)Google Scholar
  28. [TPZ02]
    Tao, Y., Papadias, D., Zhang, J.: Aggregate processing of planar points. In: Jensen, C.S., Jeffery, K., Pokorný, J., Šaltenis, S., Bertino, E., Böhm, K., Jarke, M. (eds.) EDBT 2002. LNCS, vol. 2287, p. 682. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  29. [TP02]
    Tao, Y., Papadias, D.: Time-Parameterized Queries for Spatio-Temporal Databases. In: ACM SIGMOD (2002)Google Scholar
  30. [TPS02]
    Tao, Y., Papadias, D., Shen, Q.: Continuous Nearest Neighbor Search. In: VLDB (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Yufei Tao
    • 1
  • Nikos Mamoulis
    • 2
  • Dimitris Papadias
    • 3
  1. 1.Department of Computer ScienceCarnegie Mellon UniversityUSA
  2. 2.Department of Computer Science and Information SystemsUniversity of Hong KongHong Kong
  3. 3.Department of Computer ScienceHong Kong University of Science and TechnologyHong Kong

Personalised recommendations