CRB-Tree: An Efficient Indexing Scheme for Range-Aggregate Queries

  • Sathish Govindarajan
  • Pankaj K. Agarwal
  • Lars Arge
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2572)

Abstract

We propose a new indexing scheme, called the CRB-tree, for efficiently answering range-aggregate queries. The range-aggregate problem is defined as follows: Given a set of weighted points in R d , compute the aggregate of weights of points that lie inside a d-dimensional query rectangle. In this paper we focus on range-COUNT, SUM, AVG aggregates. First, we develop an indexing scheme for answering two-dimensional range-COUNT queries that usesO(N/B) disk blocks and answers a query in O(logN B) I/Os, where N is the number of input points and B is the disk block size. This is the first optimal index structure for the 2D range- COUNT problem. The index can be extended to obtain a near-linear-size structure for answering range-SUM queries using O(logN B) I/Os.We also obtain similar bounds for rectangle-intersection aggregate queries, in which the input is a set of weighted rectangles and a query asks to compute the aggregate of the weights of those input rectangles that overlap with the query rectangle. This result immediately improves a recent result on temporal-aggregate queries. Our indexing scheme can be dynamized and extended to higher dimensions. Finally, we demonstrate the practical efficiency of our index by comparing its performance against kdB-tree. For a dataset of around 100 million points, the CRB-tree query time is 8-10 times faster than the kdB-tree query time. Furthermore, unlike other indexing schemes, the query performance of CRB-tree is oblivious to the distribution of the input points and placement, shape and size of the query rectangle.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. K. Agarwal and J. Erickson. Geometric range searching and its relatives. In B. Chazelle, J. E. Goodman, and R. Pollack, editors, Advances in Discrete and Computational Geometry, volume 223 of Contemporary Mathematics, pages 1–56. American Mathematical Society, Providence, RI, 1999.Google Scholar
  2. 2.
    A. Aggarwal and J. S. Vitter. The input/output complexity of sorting and related problems. Commun. ACM, 31:1116–1127, 1988.CrossRefMathSciNetGoogle Scholar
  3. 3.
    L. Arge. External memory data structures. In J. Abello, P. M. Pardalos, and M. G. C. Resende, editors, Handbook of Massive Data Sets, pages 313–358. Kluwer Academic Publishers, 2002.Google Scholar
  4. 4.
    L. Arge, O. Procopiuc, and J. S. Vitter. Implementing I/O-efficient data structures using TPIE. In Proc. 10th Annual European Symposium on Algorithms, pages 88–100, 2002.Google Scholar
  5. 5.
    L. Arge and J. Vahrenhold. I/O efficient dynamic planar point location. In Proc. ACM Symp. on Computational Geometry, pages 191–200, 2000.Google Scholar
  6. 6.
    C. Y. Chan and Y. E. Ioannidis. Hierarchical cubes for range-sum queries. In Proc. of 25th International Conference on Very Large DataBases, pages 675–686, 1999.Google Scholar
  7. 7.
    B. Chazelle. A functional approach to data structures and its use in multidimensional searching. SIAM J. Comput., 17(3):427–462, June 1988.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    B. Chazelle. Lower bounds for orthogonal range searching, II: The arithmetic model. J. ACM, 37:439–463, 1990.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    H. Edelsbrunner and M. H. Overmars. On the equivalence of some rectangle problems. Information Processing Letters, 14(3):124–128, 1982.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    V. Gaede and O. Günther. Multidimensional access methods. ACM Comput. Surv., 30:170–231, 1998.CrossRefGoogle Scholar
  11. 11.
    S. Geffner, D. Agarwal, and A. E. Abbadi. The dynamic datacube. In Proc of Intl. Conference on Extending Database Technology, pages 237–253, 2000.Google Scholar
  12. 12.
    V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing data cubes efficiently. In Proc. of ACM SIGMOD Intl. conference on Management of Data, pages 205–216, 1996.Google Scholar
  13. 13.
    J. Kim, S. Kang, and M. Kim. Effective temporal aggregation using point-based trees. In Database and Expert Systems Applications, pages 1018–1030, 1999.Google Scholar
  14. 14.
    N. Kline and R. T. Snodgrass. Computing temporal aggregates. In Proc. of Intl conference on Data Engineering, pages 222–231, 1995.Google Scholar
  15. 15.
    S. Lee, W. Ling, and H. Li. Hierarchical compact cubes for range-max queries. In Proc of 26th International Conference on Very Large DataBases, pages 232–241, 2000.Google Scholar
  16. 16.
    J. Nievergelt and P. Widmayer. Spatial data structures: Concepts and design choices. In J.-R. Sack and J. Urrutia, editors, Handbook of Computational Geometry, pages 725–764. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000.CrossRefGoogle Scholar
  17. 17.
    J. Robinson. The k-d-b tree: A search structure for large multidimensional dynamic indices. In Proc. of SIGMOD Conference on Management of Data, pages 10–18, 1981.Google Scholar
  18. 18.
    Y. Tao, D. Papadias, and J. Zhang. Aggregate processing of planar points. In Extending Database Technology, pages 682–700, 2002.Google Scholar
  19. 20.
    D. E. Vengroff.Atransparent parallel I/O environment. In Proc.DAGS Symposium on Parallel Computation, 1994.Google Scholar
  20. 21.
    J. Yang and J. Widom. Incremental computation and maintenance of temporal aggregates. In Proceedings of the 17th International Conference on Data Engineering, pages 51–60, 2001.Google Scholar
  21. 22.
    D. Zhang, A. Markowetz, V. Tsotras, D. Gunopulos, and B. Seeger. Efficient computation of temporal aggregates with range predicates. In Proc. Principles Of Database Systems, pages 237–245, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sathish Govindarajan
    • 1
  • Pankaj K. Agarwal
    • 1
  • Lars Arge
    • 1
  1. 1.Department of Computer ScienceDuke UniversityDurham

Personalised recommendations