Advertisement

Bkd-Tree: A Dynamic Scalable kd-Tree

  • Octavian Procopiuc
  • Pankaj K. Agarwal
  • Lars Arge
  • Jeffrey Scott Vitter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2750)

Abstract

In this paper we propose a new index structure, called the Bkd-tree, for indexing large multi-dimensional point data sets. The Bkd-tree is an I/O-efficient dynamic data structure based on the kd-tree. We present the results of an extensive experimental study showing that unlike previous attempts on making external versions of the kd-tree dynamic, the Bkd-tree maintains its high space utilization and excellent query and update performance regardless of the number of updates performed on it.

Keywords

Internal Node External Memory Query Performance Space Utilization Insertion Performance 
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. 1.
    Agarwal, P.K., Arge, L., Procopiuc, O., Vitter, J.S.: A framework for index bulk loading and dynamization. In: Proc. Intl. Colloq. Automata, Languages and Programming, pp. 115–127 (2001) Google Scholar
  2. 2.
    Aggarwal, A., Vitter, J.S.: The Input/Output complexity of sorting and related problems. Commun. ACM 31, 1116–1127 (1988)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Arge, L.: External memory data structures. In: Abello, J., Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Massive Data Sets, pp. 313–358. Kluwer, Dordrecht (2002)Google Scholar
  4. 4.
    Arge, L., Procopiuc, O., Vitter, J.S.: Implementing I/O-efficient data structures using TPIE. In: Proc. European Symp. on Algorithms, pp. 88–100 (2002) Google Scholar
  5. 5.
    Arge, L., Samoladas, V., Vitter, J.S.: On two-dimensional indexability and optimal range search indexing. In: Proc. ACM Symp. Principles of Database Systems, vol. 47, pp. 346–357 (1999) Google Scholar
  6. 6.
    Beckmann, N., Kriegel, H.-P., Schneider, R., Seeger, B.: The R*-tree: An efficient and robust access method for points and rectangles. In: Proc. SIGMOD Intl. Conf. on Management of Data, pp. 322–331 (1990) Google Scholar
  7. 7.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bentley, J.L.: Decomposable searching problems. Inform. Process. Lett. 8, 244–251 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Berchtold, S., Böhm, C., Kriegel, H.-P.: Improving the query performance of high-dimensional index structures by bulk load operations. In: Schek, H.-J., Saltor, F., Ramos, I., Alonso, G. (eds.) EDBT 1998. LNCS, vol. 1377, pp. 216–230. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Evangelidis, G., Lomet, D., Salzberg, B.: The hBΠ-tree: A multi-attribute index supporting concurrency, recovery and node consolidation. The VLDB Journal 6, 1–25 (1997) Google Scholar
  11. 11.
    Gaede, V., Günther, O.: Multidimensional access methods. ACM Computing Surveys 30(2), 170–231 (1998)CrossRefGoogle Scholar
  12. 12.
    Grossi, R., Italiano, G.F.: Efficient cross-tree for external memory. In: Abello, J., Vitter, J.S. (eds.) External Memory Algorithms and Visualization, pp. 87–106. American Mathematical Society, Providence (1999), Revised version available at ftp://ftp.di.unipi.it/pub/techreports/TR-00-16.ps.Z
  13. 13.
    Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proc. SIGMOD Intl. Conf. on Management of Data, pp. 47–57 (1984) Google Scholar
  14. 14.
    Jagadish, H.V., Narayan, P.P.S., Seshadri, S., Sudarshan, S., Kanneganti, R.: Incremental organization for data recording and warehousing. In: Proc. Intl. Conf. on Very Large Data Bases, pp. 16–25 (1997) Google Scholar
  15. 15.
    Kanth, K.V.R., Singh, A.K.: Optimal dynamic range searching in nonreplicating index structures. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 257–276. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    Lee, D.T., Wong, C.K.: Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees. Acta Informatica 9, 23–29 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Lomet, D.: B-tree page size when caching is considered. SIGMOD Record 27(3), 28–32 (1998)CrossRefGoogle Scholar
  18. 18.
    Lomet, D.B., Salzberg, B.: The hB-Tree: A multiattribute indexing method with good guaranteed performance. ACM Trans. on Database Systems 15(4), 625–658 (1990)CrossRefGoogle Scholar
  19. 19.
    Nievergelt, J., Hinterberger, H., Sevcik, K.C.: The grid file: An adaptable, symmetric multikey file structure. ACM Trans. on Database Systems 9(1), 38–71 (1984)CrossRefGoogle Scholar
  20. 20.
    O’Neil, P.E., Cheng, E., Gawlick, D., O’Neil, E.J.: The log-structured mergetree (LSM-tree). Acta Informatica, 33(4):351–385 (1996)Google Scholar
  21. 21.
    Overmars, M.: The Design of Dynamic Data Structures. LNCS, vol. 156. Springer, Heidelberg (1983)zbMATHGoogle Scholar
  22. 22.
    Robinson, T.: The K-D-B-tree: A search structure for large multidimensional dynamic indexes. In: Proc. SIGMOD Intl. Conf. on Management of Data, pp. 10–18 (1981)Google Scholar
  23. 23.
    Samet, H.: The design and analysis of spatial data structures. Addison-Wesley, Reading (1990)Google Scholar
  24. 24.
    Silva Filho, Y.V.: Average case analysis of region search in balanced k-d trees. Inform. Process. Lett. 8, 219–223 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    TIGER/Line Files, 1997 Technical Documentation. U.S. Census Bureau (1998), http://www.census.gov/geo/tiger/TIGER97D.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Octavian Procopiuc
    • 1
  • Pankaj K. Agarwal
    • 1
  • Lars Arge
    • 1
  • Jeffrey Scott Vitter
    • 2
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of Computer SciencePurdue UniversityWest LafayetteUSA

Personalised recommendations