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An application of the theory of graphs and hypergraphs to the decomposition of relational database schemes

  • J. Paredaens
  • D. van Gucht
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 159)

Abstract

An application of the theory of graphs and hypergraphs to the decomposition of Relational Database Schemas is studied.

Four new characterizations of cyclic hypergraphs are given.

Cyclic pairs of nodes are defined and it is proved that their presence characterizes cyclic hypergraphs. An algorithm to detect cyclic pairs is given.

Finally this concept is generalized to cyclic nodes and cyclic sets and it is proved that a hypergraph can be decomposed in a cyclic part and an acyclic part. In this way the acyclic part of a cyclic hypergraph can be isolated.

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Bibliography

  1. [AHU]
    A. Aho, J. Hopcroft, J. Ullman. The Design and Analysis of Computer Algorithhms., Addison-Wesley, 1974.Google Scholar
  2. [B]
    C. Berge. Graphes et Hypergraphes, Dunod, Paris, 1970.Google Scholar
  3. [BFH]
    C. Beeri, R. Fagin, J. Howard. A Complete Axiomatisation for Functional and Multivalued Dependencies in Database Relations, ACMSIGMOD Intern. Symp. on Manag. of Data, 1977.Google Scholar
  4. [BFMY]
    C. Beeri, R. Fagin, D. Maier, M. Yannakakis. On the Desirability of Acyclic Database Schemes, IBM, San Jose, RJ3131, 1981.Google Scholar
  5. [C]
    E. Codd. A Relational Model of Data for Large Shared Data Banks, CACM Vol 13, nr. 6, June 1970, p377–38?.Google Scholar
  6. [FMU]
    R. Fagin, A. Mendelzon, J. Ullman. A Simplified Universal Relation. Assumption and its Properties, IBM, San Jose, RJ2900, 1980.Google Scholar
  7. [G]
    M.H. Graham. On the Universal Relation, Technical Report, University of Toronto, September 1979.Google Scholar
  8. [H]
    F. Harary. Graph Theory, Addison-Wesley, 1972.Google Scholar
  9. [MU1]
    D. Maier, J. Ullman. Connections in Acyclic Hypergraphs, STAN-CS-81-853, 1981.Google Scholar
  10. [MU2]
    D. Maier, J. Ullman. Maximal Objects and the Semantics of Universal Relation Databases, SUNY at Stony Brook, 80-016, 1980.Google Scholar
  11. [P]
    J. Paredaens. The Interaction of Integrity Constraints in an Information System, JCSS, Vol 20, 3, p310–328, 1980.Google Scholar
  12. [P, VG]
    J. Paredaens, D. Van Gucht. An Application of the Theory of Graphs and Hypergraphs to the Decomposition of Relational Database Schemas, Universitaire Instelling Antwerpen, August 1982.Google Scholar
  13. [U]
    J. Ullman. Principles of Database Systems, Pitman, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • J. Paredaens
    • 1
  • D. van Gucht
    • 1
  1. 1.Dept. MathematicsUniversitaire Instellin AntwerpenAntwerpenBelgium

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