Minimal Representations of Directed Hypergraphs and Their Application to Database Design

  • G. Ausiello
  • A. D’Atri
  • D. Saccà
Part of the International Centre for Mechanical Sciences book series (CISM, volume 284)


In this paper the problem of minimal representations for sets of functional dependencies for relational databases is analyzed in terms of directed hypergraphs. Various concepts of minimal representations of directed hypergraphs are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs. In particular we consider coverings which are the minimal representations with respect to all parameters which may be adopted to characterize a given hypergraph (number of hyperares, number of adjacency lists required for the representation, length of the overall description, etc.). The relationships among the various minimal coverings are discussed and the computational properties are analyzed. In order to derive such results a graphic representation of hypergraphs is introduced. Applications of these results to functional dependency manipulation are finally presented.


Minimal Covering Minimal Representation Adjacency List Redundant Node Simple Node 
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  1. [1]
    Aho, A.V., Garey, M.R. and Ullman, J.D., The transitive reduction of a directed graph. SIAM J. on Computing, 1 (1972), pp. 131–137.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    Ausiello, G., D’Atri, A. and Saccà, D., Graph algorithms for functional dependency manipulation. JACM 30, 4 (Oct. 1983), pp. 752–766.CrossRefzbMATHGoogle Scholar
  3. [3]
    Batini, C. and D’Atri, A., Rewriting systems as a tool for relational data base design. LNCS 73, Springer-Verlag (1979), pp. 139–154.Google Scholar
  4. [4]
    Berge, C., Graphs and hypergraphs. North Holland, Amsterdam (1973).Google Scholar
  5. [5]
    Boley, H, Directed recursive labelnode hypergraphs: a new representa¬tion Language. Artificial Intelligence 9 (1977), pp. 49–85.CrossRefzbMATHGoogle Scholar
  6. [6]
    Fagin, R, Mendelzon, A.O. and Ullman, J.D., A simplified universal relation assumption and its properties. ACM TODS, 7,3 (1982), pp. 343–360.Google Scholar
  7. [7]
    Garey, M.R. and Johnson, D.S., Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979).zbMATHGoogle Scholar
  8. [8]
    Gnesi, S., Montanari, U. and Martelli, A., Dynamic programming as graph searching: an algebraic approach. JACM 28, 4 (1981), pp. 737–751.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    Lipski, W., Two NP-complete problems related to information retrieval. Fundamentals of Computation Theory. LNCS 56, Springer-Verlag, (1977), pp. 452–458.Google Scholar
  10. [10]
    Maier, D., Minimum covers in the relational data base model. JACM 27, 4 (1980), pp. 664–674.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    Maier, D., Descarding the universal instance assumption: preliminary results. Proc. XP1 Conf., Stony brook, NY (1980).Google Scholar
  12. [12]
    Maier, D. and Ullman, J.D., Connections in acyclic hypergraphs. 1st Symposium on Principles of Data Base Systems, Los Angeles (1982).Google Scholar
  13. [13]
    Nilsson, N.J., Problem solving methods in artificial intelligence. McGraw Hill, New York (1971).Google Scholar
  14. [14]
    Paz, A. and Moran, S., NP-optimization problems and their approximation. In Proc. 4th Int. Symp. on Automata, Languages and Programming, LNCS, Springer-Verlag, 1977.Google Scholar
  15. [15]
    Ullman, J.D., Principles of Data Base Systems. Computer Science Press, Potomac, Md. (1980).Google Scholar
  16. [16]
    Yannakakis, M., A Theory of Safe Locking Policies in Database Systems. JACM 29,3 (1982), pp. 718–740.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1984

Authors and Affiliations

  • G. Ausiello
    • 1
  • A. D’Atri
    • 1
  • D. Saccà
    • 2
  1. 1.Università “La Sapienza”RomaItaly
  2. 2.CRALRendeItaly

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