Plot Query Processing with Wavelets

  • Mehrdad Jahangiri
  • Cyrus Shahabi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5069)


Plots are among the most important and widely used tools for scientific data analysis and visualization. With a plot (a.k.a. range group-by query) data are divided into a number of groups, and at each group, they are summarized over one or more attributes for a given arbitrary range. Wavelets, on the other hand, allow efficient computation of (individual) exact and approximate aggregations. With the current practice, to generate a plot over a wavelet-transformed dataset, one aggregate query is executed per each plot point; hence, for large plots (containing numerous points) a large number of aggregate queries are submitted to the database. On the contrary, we redefine a plot as a range group-by query and propose a wavelet-based technique that exploits I/O sharing across plot points to evaluate the plot efficiently and progressively. The intuition behind our approach comes from the fact that we can decompose a plot query into two sets of 1) aggregate queries, and 2) reconstruction queries. Subsequently, we exploit and extend our earlier related studies to effectively compute both quires in the wavelet domain. We also show that our technique is not only efficient as an exact algorithm but also very effective as an approximation method where either the query time or the storage space is limited.


Discrete Wavelet Transform Range Query Query Time Wavelet Domain Reconstruction Phase 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
  2. 2.
    Chakrabarti, K., Garofalakis, M.N., Rastogi, R., Shim, K.: Approximate query processing using wavelets. In: Proc. of VLDB, pp. 111–122 (2000)Google Scholar
  3. 3.
    Chen, Z., Narasayya, V.: Efficient computation of multiple group by queries. In: SIGMOD 2005, pp. 263–274. ACM Press, New York (2005)CrossRefGoogle Scholar
  4. 4.
    Garofalakis, M., Gibbons, P.B.: Wavelet synopses with error guarantees. In: Proc. of ACM SIGMOD (2002)Google Scholar
  5. 5.
    Geffner, S., Agrawal, D., Abbadi, A.E., Smith, T.: Relative prefix sums: An efficient approach for querying dynamic OLAP data cubes. In: Proc. of ICDE (1999)Google Scholar
  6. 6.
    Gibbons, P.B., Matias, Y.: New sampling-based summary statistics for improving approximate query answers. In: Proc. of SIGMOD, pp. 331–342 (1998)Google Scholar
  7. 7.
    Gilbert, A.C., Kotidis, Y., Muthukrishnan, S., Strauss, M.J.: Optimal and approximate computation of summary statistics for range aggregates. In: Proc. of PODS (2001)Google Scholar
  8. 8.
    Gunopulos, D., Kollios, G., Tsotras, V.J., Domeniconi, C.: Approximating multidimensional aggregate range queries over real attributes. In: Proc. of SIGMOD (2000)Google Scholar
  9. 9.
    Hellerstein, J.M., Haas, P.J., Wang, H.: Online aggregation. In: Proc. of SIGMOD, pp. 171–182. ACM Press, New York (1997)CrossRefGoogle Scholar
  10. 10.
    Ho, C., Agrawal, R., Megiddo, N., Srikant, R.: Range queries in OLAP data cubes. In: Proc. of SIGMODGoogle Scholar
  11. 11.
    Jahangiri, M., Sacharidis, D., Shahabi, C.: Shift-Split: I/O Efficient Maintenance of Wavelet-Transformed Multidimensional Data. In: Proc. of SIGMOD (2005)Google Scholar
  12. 12.
    Jahangiri, M., Shahabi, C.: ProDA: A Suite of WebServices for Progressive Data Analysis. In: Proc. of ACM SIGMOD (demonstration) (2005)Google Scholar
  13. 13.
    Jahangiri, M., Shahabi, C.: Wolap: Wavelet-based range aggregate query processing. In: Department of Computer Science Technical Reports. USC (2007)Google Scholar
  14. 14.
    Lazaridis, I., Mehrotra, S.: Progressive approximate aggregate queries with a multi-resolution tree structure. In: Proc. of SIGMOD, pp. 401–412 (2001)Google Scholar
  15. 15.
    Nievergelt, Y.: Wavelets Made Easy. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  16. 16.
    Poosala, V., Ganti, V.: Fast approximate answers to aggregate queries on a data cube. In: Proc. of SSDBM, pp. 24–33. IEEE Computer Society, Los Alamitos (1999)Google Scholar
  17. 17.
    Riedewald, M., Agrawal, D., Abbadi, A.E.: pCube: Update-efficient online aggregation with progressive feedback. In: Proc. of SSDBM, pp. 95–108 (2000)Google Scholar
  18. 18.
    Schmidt, R., Shahabi, C.: How to evaluate multiple range-sum queries progressively. In: Proc. of ACM PODS, pp. 3–5 (2002)Google Scholar
  19. 19.
    Schmidt, R., Shahabi, C.: Propolyne: A fast wavelet-based technique for progressive evaluation of polynomial range-sum queries. In: Jensen, C.S., Jeffery, K.G., Pokorný, J., Šaltenis, S., Bertino, E., Böhm, K., Jarke, M. (eds.) EDBT 2002. LNCS, vol. 2287. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Shahabi, C., Jahangiri, M., Sacharidis, D.: Hybrid Query and Data Ordering for Fast and Progressive Range-Aggregate Query Answering. International Journal of Data Warehousing and Mining 1(2), 49–69 (2005)Google Scholar
  21. 21.
    Shahabi, C., Schmidt, R.: Wavelet disk placement for efficient querying of large multidimensional data sets. Technical Reports, USC (2004)Google Scholar
  22. 22.
    Vitter, J.S., Wang, M.: Approximate computation of multidimensional aggregates of sparse data using wavelets. In: Proc. of SIGMOD, pp. 193–204 (1999)Google Scholar
  23. 23.
    Wu, Y.-L., Agrawal, D., Abbadi, A.E.: Using wavelet decomposition to support progressive and approximate range-sum queries over data cubes. In: Proc. of CIKM, pp. 414–421 (2000)Google Scholar
  24. 24.
    Zhao, Y., Deshpande, P.M., Naughton, J.F., Shukla, A.: Simultaneous optimization and evaluation of multiple dimensional queries. In: Proc. of SIGMOD, pp. 271–282. ACM Press, New York (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mehrdad Jahangiri
    • 1
  • Cyrus Shahabi
    • 1
  1. 1.Computer Science DepartmentUniversity of Southern CaliforniaLos Angeles

Personalised recommendations