Skip to main content

Constructing Optimal Wavelet Synopses

  • Conference paper
Current Trends in Database Technology – EDBT 2006 (EDBT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4254))

Included in the following conference series:

Abstract

The wavelet decomposition is a proven tool for constructing concise synopses of massive data sets and rapid changing data streams, which can be used to obtain fast approximate, with accuracy guarantees, answers. In this work we present a generic formulation for the problem of constructing optimal wavelet synopses under space constraints for various error metrics, both for static and streaming data sets. We explicitly associate existing work and categorize it according to the previous problem formulation and, further, we present our current work and identify its contributions in this context. Various interesting open problems are described and our future work directions are clearly stated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. In: Proceedings ACM symposium on Theory of computing (STOC) (1996)

    Google Scholar 

  2. Cormode, G., Garofalakis, M., Sacharidis, D.: Fast approximate wavelet tracking on streams. In: Ioannidis, Y., Scholl, M.H., Schmidt, J.W., Matthes, F., Hatzopoulos, M., Böhm, K., Kemper, A., Grust, T., Böhm, C. (eds.) EDBT 2006. LNCS, vol. 3896, pp. 4–22. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Garofalakis, M., Gibbons, P.B.: Wavelet synopses with error guarantees. In: Proceedings ACM International Conference on Management of Data (SIGMOD) (2002)

    Google Scholar 

  4. Garofalakis, M., Kumar, A.: Deterministic wavelet thresholding for maximum-error metrics. In: Proceedings ACM Principles of Database Systems (PODS) (2004)

    Google Scholar 

  5. Gilbert, A.C., Kotidis, Y., Muthukrishnan, S., Strauss, M.J.: Surfing wavelets on streams: One-pass summaries for approximate aggregate queries. In: Proceedings International Conference on Very Large Data Bases (VLDB) (2001)

    Google Scholar 

  6. Guha, S.: Space efficiency in synopsis construction algorithms. In: Proceedings International Conference on Very Large Data Bases (VLDB) (2005)

    Google Scholar 

  7. Guha, S., Harb, B.: Wavelet synopsis for data streams: minimizing non-euclidean error. In: Proceedings ACM International Conference on Knowledge Discovery in Data Mining (SIGKDD) (2005)

    Google Scholar 

  8. Guha, S., Harb, B.: Approximation Algorithms for Wavelet Transform Coding of Data Streams. In: Proceedings ACM-SIAM Symposium on Discrete Algorithms (SODA) (2006)

    Google Scholar 

  9. Jahangiri, M., Sacharidis, D., Shahabi, C.: Shift-Split: I/O efficient maintenance of wavelet-transformed multidimensional data. In: Proceedings ACM International Conference on Management of Data (SIGMOD) (2005)

    Google Scholar 

  10. Karras, P., Mamoulis, N.: One-pass wavelet synopses for maximum-error metrics. In: Proceedings International Conference on Very Large Data Bases (VLDB) (2005)

    Google Scholar 

  11. Matias, Y., Urieli, D.: On the optimality of the greedy heuristic in wavelet synopses for range queries. Technical Report TR-TAU (2005)

    Google Scholar 

  12. Matias, Y., Vitter, J.S., Wang, M.: Wavelet-based histograms for selectivity estimation. In: Proceedings ACM International Conference on Management of Data (SIGMOD) (1998)

    Google Scholar 

  13. Muthukrishnan, S.: Data streams: algorithms and applications. In: Proceedings ACM Symposium of Discrete Algorithms (SODA) (2003)

    Google Scholar 

  14. Muthukrishnan, S.M.: Subquadratic algorithms for workload-aware haar wavelet synopses. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 285–296. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  15. Stollnitz, E.J., Derose, T.D., Salesin, D.H.: Wavelets for computer graphics: theory and applications. Morgan Kaufmann Publishers Inc., San Francisco (1996)

    Google Scholar 

  16. Matias, Y., Urieli, D.: Optimal workload-based weighted wavelet synopses. In: Eiter, T., Libkin, L. (eds.) ICDT 2005. LNCS, vol. 3363, pp. 368–382. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sacharidis, D. (2006). Constructing Optimal Wavelet Synopses. In: Grust, T., et al. Current Trends in Database Technology – EDBT 2006. EDBT 2006. Lecture Notes in Computer Science, vol 4254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11896548_10

Download citation

  • DOI: https://doi.org/10.1007/11896548_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46788-5

  • Online ISBN: 978-3-540-46790-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics