Split-freedom and MVD-intersection: A new characterization of multivalued dependencies having conflict-free covers

  • V. S. Lakshmanan
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 243)


Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [Li, Sc1, Sc2, BFMY]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a conflict-free cover. In [GT1] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of "split-free" sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of "intersection" of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorithms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs, thereby showing that they are interesting in their own right.


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  1. [B]
    C. BEERI, "On the membership problem for functional and multivalued dependencies", ACM TODS 5,3 (Sept. 1980), 241–259.Google Scholar
  2. [BFMY]
    C. BEERI, R. FAGIN, D. MAIER, and M. YANNAKAKIS, "On the desirability of acyclic database schemes", J. ACM 30, 3 (July 1983), 479–513.Google Scholar
  3. [BV]
    C. BEERI and M.Y. VARDI, "On the properties of join dependencies", In: Advances in Database Theory (H. Gallaire, J. Minker, and J.M. Nicolas, Eds.), Plenum Press, 1981, 25–72.Google Scholar
  4. [Fa]
    R. FAGIN, "Multivalued dependencies and a new normal form for relational databases", ACM TODS 2,3 (Sept. 1977), 262–278.Google Scholar
  5. [FMU]
    R. FAGIN, A.O. MENDELZON, and J.D. ULLMAN, "A simplified universal relation assumption and its properties", ACM TODS 7,3 (Sept. 1982), 343–360.Google Scholar
  6. [Ga]
    Z. GALIL, "An almost linear-time algorithm for computing a dependency basis in a relational database", J. ACM 29, 1 (Jan. 1982), 96–102.Google Scholar
  7. [GS]
    N. GOODMAN and O. SCHMUELI, "Syntactic characterization of tree database schemas", J. ACM 30, 4 (Oct. 1983), 767–786.Google Scholar
  8. [GT1]
    N. GOODMAN and Y.C. TAY, "Synthesizing fourth normal form relations using multivalued dependencies", Tech. Rep. TR-17-83, Aiken Computation Lab, Harvard Univ., 1983.Google Scholar
  9. [GT2]
    N. GOODMAN and Y.C. TAY, "A characterization of multivalued dependencies equivalent to a join dependency", Inform. Proc. Letters, 18 (1984), 261–266.Google Scholar
  10. [Ja]
    S. JAJODIA, "On the equivalence of relational and network models", Inform. Proc. Letters, 20 (1985), 51–54.Google Scholar
  11. [Li]
    Y.E. LIEN, "On the equivalence of database models", J. ACM 29, 2 (April 1982), 333–363.Google Scholar
  12. [Ma]
    D. MAIER, The Theory of Relational Databases, Comp. Sci. Press., Maryland, 1983.Google Scholar
  13. [Sa]
    Y. SAGIV, "An algorithm for inferring multivalued dependencies with an application to propositional logic", J. ACM 27, 2 (April 1980), 250–262.Google Scholar
  14. [Sc1]
    E. SCIORE, "Some observations of real-world data dependencies", Proc. XP1 Workshop, Stony Brook, N.Y., June 1980.Google Scholar
  15. [Sc2]
    E. SCIORE, "Real-world MVDs", In: Proc. Int. Conf. on Management of Data (April 1981), ACM N.Y., 1981, pp. 121–132.Google Scholar
  16. [Ul]
    J.D. ULLMAN, Principles of Database Systems, Comp. Sci. Press, Maryland, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • V. S. Lakshmanan
    • 1
  1. 1.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

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