An almost linear time algorithm for computing a dependency basis in a relational data base

  • Zvi Galil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


We describe an algorithm that constructs for a given set of (functional and multivalued) dependencies Σ and a set of attributes X, the dependency basis of X. The algorithm runs in time O(min(k,log p)|Σ|), where p is the number of sets in the dependency basis of X and k is the number of dependencies in Σ. A variant of the algorithm tests whether a dependency σ is implied by Σ in time O(min(k,log p) |Σ|), where p is the number of sets in the dependency basis of the left-hand side of σ that intersect the right-hand side of σ. Whenever all the dependencies in ΣU{σ} are functional dependencies these algorithms are linear time.


Relational Database Functional Dependency Propositional Logic Linear Time Algorithm Correctness Proof 
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  1. 1.
    C. Beeri, "On the Membership Problem for Multivalued Dependencies in Relational Databases," to appear in ACM Trans. on Database Systems.Google Scholar
  2. 2.
    C. Beeri, "On the Role of Data Dependencies of Relational Database Schemas," Report No. 43, Dept. of Comp. Sci., The Hebrew University, Jerusalem, Israel, January 1979.Google Scholar
  3. 3.
    C. Beeri and P.A. Bernstein, "Computational Problems Related to the Design of Normal Form Relational Schemas," ACM Trans. on Database Systems, Vol. 4, No. 1 (March 1979), pp. 30–59.Google Scholar
  4. 4.
    R. Fagin, "Multivalued Dependencies and a New Normal Form for Relational Databases," ACM Trans. on Database Systems, Vol. 2, No. 3 (September 1977), pp. 262–278.Google Scholar
  5. 5.
    K. Hagihara, M. Ito, K. Taniguchi and T. Kasami, "Decision Problems for Multivalued Dependencies in Relational Databases," SIAM J. Computing, Vol. 8, No. 2 (May 1979), pp. 247–264.Google Scholar
  6. 6.
    D.E. Knuth, The Art of Computer Programming: Fundamental Algorithms, Vol. 1, Addison-Wesley, Reading, Massachusetts, 1968.Google Scholar
  7. 7.
    Y. Sagiv, "An Algorithm for Inferring Multivalued Dependencies with an Application to Propositional Logic," Manuscript, Department of Computer Science, University of Illinois at Urbana-Champaign, to appear in JACM.Google Scholar
  8. 8.
    Y. Sagiv and R. Fagin, "An Equivalence Between Relational Database Dependencies and a Subclass of Propositional Logic," IBM Research Report RJ2500, March 1979.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Zvi Galil
    • 1
  1. 1.Department of Mathematical Sciences Computer Science DivisionTel Aviv UniversityTel AvivIsrael

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