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Efficient Discovery of Functional Dependencies and Armstrong Relations

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1777))

Abstract

In this paper, we propose a new efficient algorithm called Dep-Miner for discovering minimal non-trivial functional dependencies from large databases. Based on theoretical foundations, our approach combines the discovery of functional dependencies along with the construction of real-world Armstrong relations (without additional execution time). These relations are small Armstrong relations taking their values in the initial relation. Discovering both minimal functional dependencies and real-world Armstrong relations facilitate the tasks of database administrators when maintaining and analyzing existing databases. We evaluate Dep-Miner performances by using a new benchmark database. Experimental results show both the efficiency of our approach compared to the best current algorithm (i.e. Tane), and the usefulness of real-world Armstrong relations.

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References

  1. Autoadmin Project, Microsoft research, database group, http://www.research.microsoft.com/db.

  2. WWW page http://www.cs.helsinki.fi/research/fdk/datamining/tane.

  3. Serge Abiteboul, Richard Hull, and Victor Vianu. Foundations of Databases. Addison Wesley, 1995.

    Google Scholar 

  4. Rakesh Agrawal and Ramakrishnan Srikant. Fast algorithms for mining association rules in large databases. In Proceedings of the Twentieth International Conference on Very Large Databases, Santiago de Chile, Chile, pages 487–499, 1994.

    Google Scholar 

  5. Roberto Bayardo and Rakesh Agrawal. Mining the most interesting rules. In Proceedings of the Fifth International Conference on Knowledge Discovery & Data Mining, San Diego, CA, USA, 1999.

    Google Scholar 

  6. Catriel Beeri, Martin Dowd, Ronald Fagin, and Richard Statman. On the structure of Armstrong relations for functional dependencies. Journal of the ACM, 31(1):30–46, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  7. Catriel Beeri and Michael Kifer. An integrated approach to logical design of relational database schemes. ACM Transaction on Database Systems, 11(2):134–158, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  8. Claude Berge. Graphs and Hypergraphs. North-Holland Mathematical Library 6. American Elsevie 1976, 2d rev. ed. edition, 1976.

    Google Scholar 

  9. Philip A. Bernstein, Michael L. Brodie, Stefano Ceri, David J. DeWitt, Michael J. Franklin, Hector Garcia-Molina, Jim Gray, Gerald Held, Joseph M. Hellerstein, H. V. Jagadish, Michael Lesk, David Maier, Jeffrey F. Naughton, Hamid Pirahesh, Michael Stonebraker, and Jeffrey D. Ullman. The Asilomar report on database research. SIGMOD Record, 27(4):74–80, 1998.

    Article  Google Scholar 

  10. Surajit Chaudhuri and Vivek R. Narasayya. Autoadmin ‘what-if’ index analysis utility. In Proceedings of the ACM SIGMOD International Conference on Management of Data, Seattle, Washington, USA, pages 367–378, 1998.

    Google Scholar 

  11. E. F. Codd. Further normalization of the data base relational model. Technical Report 909, IBM Research, 1971.

    Google Scholar 

  12. Ethan Collopy and Mark Levene. Evolving example relations to satisfy functional dependencies. In Proceedings of the International Workshop on Issues and Applications of Database Technology, pages 440–447, 1998.

    Google Scholar 

  13. Stavros S. Cosmadakis, Paris C. Kanellakis, and Nicolas Spyratos. Partition semantics for relations. Journal of Computer and System Sciences, 33(2):203–233, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  14. János Demetrovics, Leonid Libkin, and Ilya B. Muchnik. Functional dependencies in relational databases: A lattice point of view. Discrete Applied Mathematics, 40:155–185, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  15. Ronald Fagin. Armstrong databases. Technical Report 5, IBM Research Laboratory, 1982.

    Google Scholar 

  16. Ronald Fagin. Horn clauses and database dependencies. Journal of the ACM, 29(4):952–985, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  17. Georg Gottlob and Leonid Libkin. Investigations on Armstrong relations, dependency inference, and excluded functional dependencies. Acta Cybernetica, 9(4):385–402, 1990.

    MATH  MathSciNet  Google Scholar 

  18. Ykä Huhtala, Juha Kärkkäinen, Pasi Porkka, and Hannu Toivonen. Efficient discovery of functional and approximate dependencies using partitions. In Proceedings of the Fourteenth IEEE International Conference on Data Engineering, pages 392–401, 1998.

    Google Scholar 

  19. Martti Kantola, Heikki Mannila, Kari-Jouko Räihä, and Harri Siirtola. Discovering functional and inclusion dependencies in relational databases. International Journal of Intelligent Systems, 7:591–607, 1992.

    Article  MATH  Google Scholar 

  20. Mika Klemettinen, Heikki Mannila, Pirjo Ronkainen, Hannu Toivonen, and A. Inkeri Verkamo. Finding interesting rules from large sets of discovered association rules. In Proceedings of the Third International Conference on Information and Knowledge Management, Gaithersburg, Maryland, pages 401–407, 1994.

    Google Scholar 

  21. Mark Levene and Georges Loizou. A Guided Tour of Relational Databases and Beyond. Springer-verlag London Limited, 1999.

    Google Scholar 

  22. Stéphane Lopes, Jean-Marc Petit, and Lotfi Lakhal. Efficient discovery of functional dependencies and armstrong relations (complete version) http://libd2.univ-bpclermont.fr/publications. Technical report, LIMOS, 1999.

  23. Stéphane Lopes, Jean-Marc Petit, and Farouk Toumani. Discovery of “interesting” data dependencies from a workload of SQL statements (poster). In Jan M. Zytkow and Jan Rauch, editors, Proceedings of the Principles of Data Mining and Knowledge Discovery, Prague, Czech Republic, volume 1704, pages 430–435, 1999.

    Google Scholar 

  24. Heikki Mannila and Kari-Jouko Räihä. Design by example: An application of Armstrong relations. Journal of Computer and System Sciences, 33(2):126–141, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  25. Heikki Mannila and Kari-Jouko Räihä. Algorithms for inferring functional dependencies from relations. Data and Knowledge Engineering, 12(1):83–99, 1994.

    Article  MATH  Google Scholar 

  26. Heikki Mannila and Kari-Jouko Räihä. The Design of Relational Databases. Addison Wesley, 1994.

    Google Scholar 

  27. Heikki Mannila and Hannu Toivonen. Levelwise search and borders of theories in knowledge discovery. Data Mining and Knowledge Discovery, 1(3):241–258, 1997.

    Article  Google Scholar 

  28. V.M. Markowitz and J.A. Makowsky. Identifying extended entity-relationship object structures in relational schemas. IEEE Transactions on Software Engineering, 16(8):777–790, 1990.

    Article  Google Scholar 

  29. Nicolas Pasquier, Yves Bastide, Rafik Taouil, and Lotfi Lakhal. Discovering frequent closed itemsets for association rules. In Proceedings of the Seventh International Conference on Database Theory, Jerusalem, Israël, pages 398–416, 1999.

    Google Scholar 

  30. Nicolas Pasquier, Yves Bastide, Rafik Taouil, and Lotfi Lakhal. Mining bases for association rules using galois closed sets (poster). In Proceedings of the Sixteenth IEEE International Conference on Data Engineering, February 29–March 3, San Diego, CA, USA. IEEE Computer Society, 2000.

    Google Scholar 

  31. Iztok Savnik and Peter A. Flach. Bottom-up induction of functional dependencies from relations. In Proceedings of the AAAI-93Workshop on Knowledge Discovery in Databases, pages 174–185, 1993.

    Google Scholar 

  32. Nicolas Spyratos. The partition model: A deductive database model. ACM Transaction on Database Systems, 12(1):1–37, 1987.

    Article  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Lopes, S., Petit, JM., Lakhal, L. (2000). Efficient Discovery of Functional Dependencies and Armstrong Relations. In: Zaniolo, C., Lockemann, P.C., Scholl, M.H., Grust, T. (eds) Advances in Database Technology — EDBT 2000. EDBT 2000. Lecture Notes in Computer Science, vol 1777. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46439-5_24

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  • DOI: https://doi.org/10.1007/3-540-46439-5_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67227-2

  • Online ISBN: 978-3-540-46439-6

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