Skip to main content
Log in

Functional dependencies are helpful for partial materialization of data cubes

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Functional dependencies (FD’s) are a powerful concept in data organization. They have been proven very useful in e.g., relational databases for reducing data redundancy. Little work however has been done so far for using them in the context of data cubes. In the present paper, we propose to characterize the parts of a data cube to be materialized with the help of the FD’s present in the underlying data. For this purpose, we consider two applications: (i) how to choose the best cuboids of a data cube to materialize in order to guarantee a fixed performance of query evaluation and, (ii) how to choose the best tuples, hence partial cuboids, in order to reduce the size of the data cube without loosing information. In both cases FD’s turn to be fundamental in characterizing the solutions of these problems.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading, MA (1995)

    MATH  Google Scholar 

  2. Agarwal, S., Agrawal, R., Deshpande, P., Gupta, A., Naughton, J.F., Ramakrishnan, R., Sarawagi, S.: On the computation of multidimensional aggregates. In: Proceedings of VLDB Conference, pp. 506–521. Morgan Kaufmann, San Mateo (1996)

    Google Scholar 

  3. Agrawal, R., Srikant, R.: Fast algorithms for mining association rules in large databases. In: Proceedings of VLDB Conference, pp. 487–499. Morgan Kaufmann, San Mateo (1994)

    Google Scholar 

  4. Baralis, E., Paraboschi, S., Teniente, E.: Materialized view selection in a multidimensional database. In: Proceedings of VLDB Conference, pp. 156–165. Morgan Kaufmann, San Mateo (1997)

    Google Scholar 

  5. Bauer, A., Lehner, W.: On solving the view selection problem in distributed data warehouse architectures. In: Proceedings of SSDBM Conference, pp. 43–54. IEEE Computer Society Press, Los Alamitos (2003)

    Google Scholar 

  6. Beeri, C., Bernstein, P.A., Goodman, N.: A sophisticate’s introduction to database normalization theory. In: Proceedings of VLDB Conference, pp. 113–124. IEEE Computer Society Press, Los Alamitos (1978)

    Google Scholar 

  7. Blakeley, J.A., Larson, PÅ., Tompa, F.W.: Efficiently updating materialized views. In: Proceedings of SIGMOD Conference, pp. 61–71. ACM (1986)

  8. Bravo, L., Fan, W., Ma, S.: Extending dependencies with conditions. In: Proceedings of VLDB Conference, pp. 243–254. ACM (2007)

  9. Bruno, N.: Automated Physical Database Design and Tuning. CRC Press Inc, Boca Raton (2011)

    MATH  Google Scholar 

  10. Casali, A., Cicchetti, R., Lakhal, L.: Extracting semantics from data cubes using cube transversals and closures. In: Proceedings of ACM KDD Conference, pp. 69–78. ACM (2003)

  11. Casali, A., Nedjar, S., Cicchetti, R., Lakhal, L.: Closed cube lattices. In: New Trends in Data Warehousing and Data Analysis, Annals of Information Systems, vol. 3, pp. 1–20. Springer (2009)

  12. Chaudhuri, S., Lee, H., Narasayya, V.R.: Variance aware optimization of parameterized queries. In: Proceedings of SIGMOD Conference, pp. 531–542. ACM (2010)

  13. Chiang, F., Miller, R.J.: Discovering data quality rules. In: Proceedings of VLDB Conference, pp. 1166–1177 (2008)

  14. Chvatàl, V.: A greedy heuristic for the set-covering problem. Math. Oper. Res. 4(3), 233–235 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  15. Codd, E., Codd, S., Salley, C.: Providing OLAP (On-Line Analytical Processing) to User-Analysts: An IT Mandate. Tech. rep., Codd & Date, Inc (1993)

  16. Codd, E.F.: Normalized Data Base Structure: A Brief Tutorial. IBM Research Report, San Jose, California RJ935 (1971)

  17. Codd, E.F.: A relational model of data for large shared data banks (reprint). Commun. ACM 26(1), 64–69 (1983)

    Article  Google Scholar 

  18. De Bra, P., Paredaens, J.: Conditional dependencies for horizontal decompositions. In: Proceedings of ICALP Conference, LNCS, vol. 154, pp. 67–82. Springer (1983)

  19. Fan, W., Geerts, F., Li, J., Xiong, M.: Discovering conditional functional dependencies. IEEE Trans. Knowl. Data Eng. 23(5), 683–698 (2011)

    Article  Google Scholar 

  20. Florescu, D., Kossmann, D.: Rethinking cost and performance of database systems. SIGMOD Rec. 38(1), 43–48 (2009)

    Article  Google Scholar 

  21. Giannella, C., Robertson, E.L.: On approximation measures for functional dependencies. Inf. Syst. 29(6), 483–507 (2004)

    Article  Google Scholar 

  22. Golab, L., Karloff, H.J., Korn, F., Srivastava, D., Yu, B.: On generating near-optimal tableaux for conditional functional dependencies. In: Proceedings VLDB Conference, pp. 376–390 (2008)

  23. Graefe, G.: Query evaluation techniques for large databases. ACM Comput. Surv. 25(2), 73–170 (1993)

    Article  Google Scholar 

  24. Gray, J., Chaudhuri, S., Bosworth, A., Layman, A., Reichart, D., Venkatrao, M,, Pellow, F., Pirahesh, H.: Data cube: a relational aggregation operator generalizing group-by, cross-tab, and sub totals. Data Min. Knowl. Discov. 1(1), 29–53 (1997)

    Article  Google Scholar 

  25. Hanusse, N., Maabout, S., Tofan, R.: A view selection algorithm with performance guarantee. In: Proceedings of EDBT Conference, vol. 360, pp. 946–957. ACM (2009)

  26. Hanusse, N., Maabout, S., Tofan, R.: Revisiting the partial data cube materialization. In: Proceedings of ADBIS Conference, LNCS, vol. 6909, pp. 70–83. Springer (2011)

  27. Harinarayan, V., Rajaraman, A., Ullman, J.: Implementing data cubes efficiently. In: Proceedings of SIGMOD Conference, pp. 205–216. ACM Press (1996)

  28. Huhtala, Y., Kärkkäinen, J., Porkka, P., Toivonen, H.: Tane: an efficient algorithm for discovering functional and approximate dependencies. Comput. J. 42(2), 100–111 (1999)

    Article  MATH  Google Scholar 

  29. Karloff, H., Mihail, M.: On the complexity of the view-selection problem. In: Proceedings of PODS Conference, pp. 167–173. ACM (1999)

  30. Kivinen, J., Mannila, H.: Approximate inference of functional dependencies from relations. Theor. Comput. Sci. 149(1), 129–149 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  31. Lakshmanan, L., Pei, J., Han, J.: Quotient cube: how to summarize the semantics of a data cube. In: Proceedings of VLDB Conference, pp. 778–789. VLDB Endowment (2002)

  32. Lehner, W., Albrecht, J., Wedekind, H.: Normal forms for multidimensional databases. In: Proceedings of SSDBM Conference, pp. 63–72. IEEE Computer Society (1998)

  33. Li, J., Talebi, Z., Chirkova, R., Fathi, Y.: A formal model for the problem of view selection for aggregate queries. In: Proceedings of ADBIS Conference, LNCS, vol. 3631, pp. 125–138. Springer (2005)

  34. Liang, W., Wang, H., Orlowska, M.E.: Materialized view selection under the maintenance time constraint. Data Knowl. Eng. 37(2), 203–216 (2001)

    Article  MATH  Google Scholar 

  35. Mannila, H., Räihä, K.J.: Design of Relational Databases. Addison-Wesley (1992)

  36. Microsoft: Sql server: database engine tuning advisor. Available from msdn.microsoft.com/en-us/library/ms173494.aspx (2008).

  37. Niemi, T., Nummenmaa, J., Thanisch, P.: Normalising olap cubes for controlling sparsity. Data Knowl. Eng. 46(3), 317–343 (2003)

    Article  Google Scholar 

  38. Novelli, N., Cicchetti, R.: Fun: an efficient algorithm for mining functional and embedded dependencies. In: Proceedings of ICDT Conference, LNCS, vol. 1973, pp. 189–203. Springer (2001)

  39. Oracle: Oracle sql access advisor. Available from www.oracle-base.com/articles/11g/SQLAccessAdvisor_11gR1.php (2010)

  40. Ross, K.A., Srivastava, D.: Fast computation of sparse datacubes. In: Proceedings of VLDB Conference, pp. 116–125. Morgan Kaufmann (1997)

  41. Saint-Paul, R., Raschia, G., Mouaddib, N.: General purpose database summarization. In: Proceedings of VLDB Conference, pp. 733–744. ACM (2005)

  42. Shukla, A., Deshpande, P., Naughton, J.: Materialized view selection for multidimensional datasets. In: Proceedings of VLDB Conference, pp. 488–499. Morgan Kaufmann (1998)

  43. Shukla, A., Deshpande, P., Naughton, J.: Materialized View selection for multi-cube data models. In: Proceedings of EDBT Conference, LNCS, vol. 1777, pp. 269–284. Springer (2000)

  44. Thalheim, B.: Entity-Relationship Modeling: Foundations of Database Technologies. Springer (2010)

  45. Wang, W., Feng, J., Lu, H., Yu, J.: Condensed cube: an effective approach to reducing data cube size. In: Proceedings of ICDE Conference, pp. 155–165. IEEE (2002)

  46. Xin, D., Shao, Z., Han, J., Liu, H.: C-cubing: efficient computation of closed cubes by aggregation-based checking. In: Proceedings of ICDE Conference. IEEE, Computer Society (2006)

  47. Zhao, Y., Deshpande, P., Naughton, J.F.: An array-based algorithm for simultaneous multidimensional aggregates. In: Proceedings of SIGMOD Conference, pp. 159–170. ACM Press (1997)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eve Garnaud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Garnaud, E., Maabout, S. & Mosbah, M. Functional dependencies are helpful for partial materialization of data cubes. Ann Math Artif Intell 73, 245–274 (2015). https://doi.org/10.1007/s10472-013-9375-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-013-9375-5

Keywords

Mathematics Subject Classification (2010)

Navigation