Skip to main content
SpringerLink
Log in

On the desirability of γ-acyclic BCNF database schemes

  • Contributed Papers
  • Conference paper
  • First Online:
ICDT '86 (ICDT 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 243))

Included in the following conference series:

Abstract

In this paper, we show that γ-acyclic Boyce-Codd Normal Form database schemes are highly desirable with respect to query processing and updates. We first prove that this class of schemes is bounded with respect to the set of functional dependencies embodied in the database scheme. This result enlarges the class of known bounded database schemes. We then show that this class of schemes is simple in semantics by proving that there is a simple and efficient way to compute the X-total projection of the representative instance. As a consequence, answers to many queries for this class of schemes can be computed easily and efficiently. We also show that if a γ-acyclic Boyce-Codd Normal Form database scheme is lossless, then it is connection-trap-free. Finally, we derive a simple and efficient algorithm that determines if an updated state is consistent. This allows the system to enforce the satisfaction of functional dependencies embodied in the database scheme incrementally and efficiently.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A.V., Beeri, C., Ullman, J.D. “The Theory of Joins in Relational Databases.” ACM TODS 4, 3, September 1979, pp. 297–314.

    Google Scholar 

  2. Atzeni, P., Chan E.P.F. “Efficient Query Answering in the Representative Instance Approach.” Proc. ACM PODS 1985, pp. 181–188.

    Google Scholar 

  3. Berge, C. Graphs and Hypergraphs. North-Holland, Amsterdam, The Netherlands, 1973.

    Google Scholar 

  4. Beeri, C., Bernstein, P.A. “Computational Problems Related to the Design of Normal Form Relational Schemas.” ACM TODS 4, 1, March 1979, pp. 30–59.

    Google Scholar 

  5. Bernstein, P.A., Blaustein, B.T., Clarke, E.M. “Fast Maintenance of Semantic Integrity Assertions using Redundant Aggregate Data.” Proc. VLDB 1980, pp. 126–136.

    Google Scholar 

  6. Beeri, C., Bernstein, P.A., and Goodman, N. “A Sophisticate's Introduction to Database Normalization Theory.” Proc. VLDB 1978, pp. 113–124.

    Google Scholar 

  7. Biskup, J., Dayal, U., and Bernstein, P.A. “Synthesizing Independent Database Schemas.” Proc. ACM-SIGMOD 1979, Boston, Ma., pp. 143–151.

    Google Scholar 

  8. Bernstein, P.A., Goodman, N. “What Does Boyce-Codd Normal Form Do?” Proc. VLDB 1980, pp. 245–259.

    Google Scholar 

  9. Beeri, C., Vardi, M.Y. “A Proof Procedure for Data Dependencies.” JACM 31, 4, October 1984, pp. 718–741.

    Google Scholar 

  10. Chan, E.P.F. “Optimal Computation of Total Projections with Unions of Simple Chase Join Expressions.” Proc. ACM-SIGMOD 1984, Boston, Ma., pp. 149–163.

    Google Scholar 

  11. Chan, E.P.F. “An Incremental Approach to Testing Satisfaction of Functional Dependencies.” Unpublished manuscript, University of Toronto, 1981.

    Google Scholar 

  12. Chan, E.P.F., Atzeni, P. “On the Properties and Characterization of Connection-trap-free Schemes.” Proc. PODS 1986, pp. 140–147.

    Google Scholar 

  13. Chan, E.P.F., Hernańdez, H.J. “On the Desirability of γ-acyclic BCNF Database Schemes.” Submitted to Theoretical Computer Science.

    Google Scholar 

  14. Chan, E.P.F., Mendelzon, A.O. “Answering Queries on the Embedded-complete Database Schemes.” Unpublished manuscript, 1984.

    Google Scholar 

  15. Codd, E.F. “A Relational Model for Large Shared Data Banks.” CACM 13, 6 (June 1970), pp. 377–387.

    Google Scholar 

  16. Date, C.J. An Introduction to Database Systems. 3rd. edition, Reading, Ma., Addison-Wesley, 1981.

    Google Scholar 

  17. D'Atri, A., Moscarini, M. “Acyclic Hypergraphs: Their Recognition and Top-down vs. Bottom-up Generation.” IASI-CNR, R.29, Rome, Italy, 1982.

    Google Scholar 

  18. Fagin, R. “Hypergraphs and Relational Database Schemes.” JACM 30, 3, July 1983, pp. 514–550.

    Google Scholar 

  19. Graham, M.H., Mendelzon, A.O. “On Total Projections Computable by Relational Algebra.” Unpublished manuscript, Department of Computer Science, University of Toronto, August 1982.

    Google Scholar 

  20. Graham, M.H., Mendelzon, A.O., and Vardi, M.Y. “Notions of Dependency Satisfaction.” JACM 33, 1, January 1986, pp. 105–129.

    Google Scholar 

  21. Graham, M.H., Yannakakis, M. "Independent Database Schemas." JCSS 28, pp. 121–141 (1984).

    Google Scholar 

  22. Honeyman, P. "Extension Joins." Proc. VLDB 1980, pp. 239–244.

    Google Scholar 

  23. Honeyman, P. "Testing Satisfaction of Functional Dependencies." JACM 29, 3, July 1982, pp. 668–677.

    Google Scholar 

  24. Ito, M., Iwasaki, M., Kasami, T. "Some Results on the Representative Instance in Relational Databases." SIAM J. of Computing 14, 2 (1985), pp. 334–354.

    Google Scholar 

  25. LeDoux, C.H., Parker, D.S. "Reflections on Boyce-Codd Normal Form." Proc. VLDB 1982, pp. 131–141.

    Google Scholar 

  26. Lucchesi, C.L., Osborn, S.L. "Candidate Keys for Relations." JCSS 17, 2, October 1978, pp. 270–279.

    Google Scholar 

  27. Mendelzon, A.O. "Database States and their Tableaux." ACM TODS 9, 2, June 1984, pp. 264–282.

    Google Scholar 

  28. Maier, D. The Theory of Relational Databases. Computer Science Press, 1983.

    Google Scholar 

  29. Maier, D., Mendelzon, A.O., and Sagiv, Y. "Testing Implications of Data Dependencies." ACM TODS 4, 4, December 1979, pp. 455–469.

    Google Scholar 

  30. Maier, D., Rozenshtein, D., Warren, D.S. "Windows On the World." Proc. ACM-SIGMOD 1983, pp. 68–78.

    Google Scholar 

  31. Maier, D., Ullman, J.D., and Vardi, M.Y. "On the Foundations of the Universal Relation Model." ACM TODS 9, 2, June 1984, pp. 283–308.

    Google Scholar 

  32. Nicholas, J-M, Gallaire, H. "Data Bases: Theory vs Interpretation." Logic and Data Bases, Plenum Press, pp. 33–54.

    Google Scholar 

  33. Osborn, S.L. "Testing for Existence of a Covering Boyce-Codd Normal Form." IPL 8, 1, January 1979, pp. 11–14.

    Google Scholar 

  34. Sagiv, Y. "Can We Use the Universal Instance Assumption Without Using Nulls?" Proc. ACM-SIGMOD 1981, pp. 108–120.

    Google Scholar 

  35. Sagiv, Y. "A Characterization of Globally Consistent Databases and their Correct Access Paths." ACM TODS 8, 2, June 1983, pp. 266–286.

    Google Scholar 

  36. Sagiv, Y. "Evaluation of Queries in Independent Database Schemes." Unpublished manuscript, 1984.

    Google Scholar 

  37. Stonebraker, M.R. "Implementation of Integrity Constraints and Views by Query Modification." Proc. ACM-SIGMOD 1975, pp. 65–78.

    Google Scholar 

  38. Ullman, J.D. Principles of Database Systems. 2nd. edition, Computer Science Press, 1982.

    Google Scholar 

  39. Vassiliou, Y. "A Formal Treatment of Imperfect Information in Data Management." CSRG TR-123, University of Toronto, Nov. 1980.

    Google Scholar 

  40. Yannakakis, M. "Algorithms for Acyclic Database Schemes." Proc. VLDB 1981, pp. 82–94.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Science, The University of Alberta, T6G 2H1, Edmonton, Alberta, Canada

    Edward P. F. Chan & Héctor J. Hernández

Authors
  1. Edward P. F. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Héctor J. Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giorgio Ausiello Paolo Atzeni

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chan, E.P.F., Hernández, H.J. (1986). On the desirability of γ-acyclic BCNF database schemes. In: Ausiello, G., Atzeni, P. (eds) ICDT '86. ICDT 1986. Lecture Notes in Computer Science, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17187-8_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-17187-8_32

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17187-4

  • Online ISBN: 978-3-540-47346-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation