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Derivation of constraints and database relations

  • David Cohen
  • Marc Gyssens
  • Peter Jeavons
Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1118)

Abstract

In this paper we investigate which constraints may be derived from a given set of constraints. We show that, given a set of relations \(\mathcal{R}\), all of which are invariant under some set of permutations P, it is possible to derive any other relation which is invariant under P, using only the projection, Cartesian product, and selection operators, together with the effective domain of \(\mathcal{R}\), provided that the effective domain contains at least three elements. Furthermore, we show that the condition imposed on the effective domain cannot be removed. This result sharpens an earlier result of Paredaens [13], in that the union operator turns out to be superfluous. In the context of constraint satisfaction problems, this result shows that a constraint may be derived from a given set of constraints containing the binary disequality constraint if and only if it is closed under the same permutations as the given set of constraints.

Keywords

Relational database relational algebra constraint derivation 

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References

  1. 1.
    F. Bancilhon. On the completeness of query languages for relational data bases. In Proceedings 7th International Symposium on Mathematical Foundations of Computer Science (Zakopane, Poland), Lecture Notes in Computer Science, 64, Springer-Verlag, Berlin/New York, 1978, pp. 112–123.Google Scholar
  2. 2.
    W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35, 1988, pp. 401–413.Google Scholar
  3. 3.
    D. Cohen, P. Jeavons, M. Gyssens. Derivation of constraints and database relations. Technical Report CSD-TR-96-01, Royal Holloway, Univ. of London, January 1996.Google Scholar
  4. 4.
    R. Dechter. Decomposing a relation into a tree of binary relations. Journal of Computer and System Sciences, 41, 1990, pp. 2–24.Google Scholar
  5. 5.
    E.C. Freuder. A sufficient condition for backtrack-bounded search. Journal of the ACM, 32, 1985, pp. 755–761.Google Scholar
  6. 6.
    M. Gyssens, P.G. Jeavons, and D.A. Cohen. Decomposing constraint satisfaction problems using database techniques. Artificial Intelligence, 66, 1994, pp. 57–89.Google Scholar
  7. 7.
    R.M. Haralick and L.G. Shapiro. The consistent labeling problem: Part I. IEEE Trans. Pattern. Anal. Mach. Intell., 1, 1979, pp. 173–184.Google Scholar
  8. 8.
    P.G. Jeavons. On the algebraic structure of combinatorial problems. Technical Report CSD-TR-95-15, Royal Holloway, Univ. of London, October 1995.Google Scholar
  9. 9.
    P. Jeavons, D. Cohen, and M. Gyssens. A structural decomposition for hypergraphs. In Proceedings Jerusalem Combinatorics '93, H. Barcelo and G. Kalai, eds. Contemporary Mathematics, 178, 1994, pp. 161–177.Google Scholar
  10. 10.
    P. Jeavons, D. Cohen, and M. Gyssens. A unifying framework for tractable constraints. In Proceedings CP '95, Lecture Notes in Computer Science, 976, Springer-Verlag, Berlin/New York, 1995, pp. 276–291.Google Scholar
  11. 11.
    A.K. Mackworth. Consistency in networks of relations. Artificial Intelligence, 8, 1977, pp. 99–118.Google Scholar
  12. 12.
    U. Montanari. Networks of constraints: fundamental properties and applications to picture processing. Information Sciences, 7, 1974, pp. 95–132.Google Scholar
  13. 13.
    J. Paredaens. On the expressive power of the relational algebra. Information Processing Letters, 7:2, 1978, pp. 107–111.Google Scholar
  14. 14.
    J.D. Ullman. Principles of Database and Knowledge Base Systems, Vols. I and II. Computer Science Press, Rockville, Maryland, 1988 and 1989.Google Scholar
  15. 15.
    Y. Zhang and A.K. Mackworth. Parallel and distributed algorithms for finite constraint satisfaction problems. In Proceedings 3rd IEEE Symposium on Parallel and Distributed Computing (Dallas, Texas), 1991, pp. 394–397.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • David Cohen
    • 1
  • Marc Gyssens
    • 2
  • Peter Jeavons
    • 1
  1. 1.Department of Computer Science, Royal HollowayUniversity of LondonUK
  2. 2.Department WNIUniversity of LimburgDiepenbeekBelgium

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