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Acyclic database schemes (of various degrees): A painless introduction

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CAAP'83 (CAAP 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 159))

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Abstract

Database schemes (which, intuitively, are collections of table skeletons) can be viewed as hypergraphs. (A hypergraph is a generalization of an ordinary undirected graph, such that an edge need not contain exactly two nodes, but can instead contain an arbitrary nonzero number of nodes.) Unlike the situation for ordinary undirected graphs, there are several natural, nonequivalent notions of acyclicity for hypergraphs (and hence for database schemes). A large number of desirable properties of database schemes fall into a small number of equivalence classes, each completely characterized by the degree of acyclicity of the scheme. This paper is intended to be an informal introduction, in which the focus is mainly on the originally studied (and least restrictive) degree of acyclicity.

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References

  1. Aho, A. V., C. Beeri, and J. D. Ullman, "The theory of joins in relational databases," ACM Trans. on Database Systems 4,3 (1979), 297–314.

    Article  Google Scholar 

  2. Ausiello, G., A. d'Atri, and M. Moscarini, "Minimal coverings of acyclic database schemata", Proc. ONERA-CERT Toulouse Workshop on Logical Bases for Data Bases (Dec. 1982).

    Google Scholar 

  3. Batini, C., A. D'Atri, and M. Moscarini, "Formal tools for top-down and bottom-up generation of acyclic relational schemata", Proc. 7th Int. Conf. on Graph-Theoretic Concepts in Computer Science, Linz (1981).

    Google Scholar 

  4. Beeri, C., R. Fagin, D. Maier, A. O. Mendelzon, J. D. Ullman, and M. Yannakakis, "Properties of acyclic database schemes," Proc. Thirteenth Annual ACM Symposium on the Theory of Computing, 355–362 (1981).

    Google Scholar 

  5. Beeri, C., R. Fagin, D. Maier, and M. Yannakakis, "On the desirability of acyclic database schemes," J. ACM, to appear.

    Google Scholar 

  6. Bernstein, P. A. and D. W. Chiu, "Using semi-joins to solve relational queries", J. ACM 28, 1 (Jan. 1981), 25–40.

    Article  Google Scholar 

  7. Bernstein, P. A. and N. Goodman, "The power of natural semijoins" SIAM J. Computing 10,4 (Nov. 1981), 751–771.

    Article  Google Scholar 

  8. Biskup, J. and H. H. Bruggemann, "Towards designing acyclic database schemas", Proc. ONERA-CERT Toulouse Workshop on Logical Bases for Data Bases (Dec. 1982).

    Google Scholar 

  9. Chamberlin, D.D., M. M. Astrahan, K. P. Eswaran, P. P. Griffiths, R. A. Lorie, J. W. Mehl, P. Reisner, and B. W. Wade, "SEQUEL 2: A unified approach to data definition, manipulation, and control," IBM J. of Research and Development 20,6 (Nov. 1976), 560–575.

    Google Scholar 

  10. Chase, K., "Join graphs and acyclic data base schemes", Proc. 1981 Very Large Data Bases Conf., 95–100.

    Google Scholar 

  11. Codd, E. F., "A relational model for large shared data banks," Comm. ACM 13,6 (1970), 377–387.

    Article  Google Scholar 

  12. Codd, E. F., "Further normalization of the database relational model," Courant Computer Science Symposia 6: Data Base Systems, (May 24–25, 1971), Prentice-Hall, 65–98.

    Google Scholar 

  13. D'Atri, A. and M. Moscarini, "Acyclic hypergraphs: their recognition and top-down vs bottom-up generation," Consiglio Nazionale Delle Ricerche, Istituto di Analisi dei Sistemi ed Informatica, R.29 (1982).

    Google Scholar 

  14. Fagin, R., "Multivalued dependencies and a new normal form for relational databases," ACM Trans. on Database Systems 2,3 (1977), 262–278.

    Article  Google Scholar 

  15. Fagin, R., "A normal form for relational databases that is based on domains and keys," ACM Trans. on Database Systems 6,3 (Sept. 1981), 387–415.

    Article  Google Scholar 

  16. Fagin, R., "Degrees of acyclicity for hypergraphs and relational database schemes". To appear, J. ACM.

    Google Scholar 

  17. Fagin, R., A. O. Mendelzon, and J. D. Ullman, "A simplified universal relation assumption and its properties," ACM Trans. on Database Systems 7,3 (Sept. 1982), 343–360.

    Article  Google Scholar 

  18. Finkelstein, S., private communication.

    Google Scholar 

  19. Goodman, N., and O. Shmueli, "The tree property is fundamental for query processing", Proc. First ACM SIGACT-SIGMOD Principles of Database Systems (1982), Los Angeles, 40–48.

    Google Scholar 

  20. Goodman, N., and O. Shmueli, "Transforming cyclic schemas into trees", Proc. First ACM SIGACT-SIGMOD Principles of Database Systems (1982), Los Angeles, 49–54.

    Google Scholar 

  21. Goodman, N., and O. Shmueli, "Tree queries: a simple class of queries," ACM Trans. on Database Systems 7,4 (Dec. 1982), 653–677.

    Article  Google Scholar 

  22. Goodman, N., O. Shmueli, and Y. C. Tay, "GYO reductions, canonical connections, and cyclic schemas and tree projections", Proc. Second ACM SIGACT-SIGMOD Principles of Database Systems (1983), Atlanta, 267–278.

    Google Scholar 

  23. Graham, M. H., "On the universal relation," Technical Report, Univ. of Toronto (Sept. 1979).

    Google Scholar 

  24. Gyssens, M. and J. Paredaens, "A decomposition methodology for cyclic databases", Proc. ONERA-CERT Toulouse Workshop on Logical Bases for Data Bases (Dec. 1982).

    Google Scholar 

  25. Hanatani, Y., "Eliminating cyclies in database schemas", Proc. ONERA-CERT Toulouse Workshop on Logical Bases for Data Bases (Dec. 1982).

    Google Scholar 

  26. Honeyman, P., R. E. Ladner, and M. Yannakakis, "Testing the universal instance assumption," Inf. Proc. Letters, 10:1 (1980), 14–19.

    Article  Google Scholar 

  27. Hull, R., "Acyclic join dependency and database projections," USC Technical Report (June 1981).

    Google Scholar 

  28. Maier, D., Y. Sagiv, and M. Yannakakis, "On the complexity of testing implications of functional and join dependencies", J. ACM 28,4 (Oct. 1981), 680–695.

    Article  Google Scholar 

  29. Maier, D. and J. D. Ullman, "Connections in acyclic hypergraphs," Proc. First ACM SIGACT-SIGMOD Principles of Database Systems (1982), Los Angeles, 34–39.

    Google Scholar 

  30. Ozkarahan, E. A., S. A. Schuster, and K. C. Sevick, "Performance evaluation of a relational associative processor", ACM Trans. on Database Systems 2,2 (June 1977), 175–196.

    Article  Google Scholar 

  31. Rissanen, J., "Theory of relations for databases — a tutorial survey." Proc. 7th Symp. on Math. Found. of Comp. Science, Lecture Notes in Comp. Science, 64 (1978), Springer-Verlag, 537–551.

    Google Scholar 

  32. Rothnie, J. B. Jr., P. A. Bernstein, S. Fox, N. Goodman, M. Hammer, T. A. Landers, C. Reeve, D. W. Shipman, and E. Wong, "Introduction to a system for distributed databases (SDD-1)", ACM Trans. on Database Systems 5,1 (Mar. 1980), 1–17.

    Article  Google Scholar 

  33. Sacca, D., "On the recognition of coverings of acyclic database hypergraphs", Proc. Second ACM SIGACT-SIGMOD Principles of Database Systems (1983), Atlanta, 297–304.

    Google Scholar 

  34. Tarjan, R. E., and Yannakakis, M., "Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs", Bell Labs Technical Report (March 1982), Murray Hill, New Jersey.

    Google Scholar 

  35. Ullman, J. D., "The U.R. strikes back," Proc. First ACM SIGACT-SIGMOD Principles of Database Systems (1982), Los Angeles, 10–22.

    Google Scholar 

  36. Yannakakis, M., "Algorithms for acyclic database schemes," Proc. 1981 Very Large Data Bases Conf., 82–94.

    Google Scholar 

  37. Yu, C.T. and M.Z. Ozsoyoglu, "An algorithm for tree-query membership of a distributed query", Proc. 1979 IEEE COMPSAC, 306–312.

    Google Scholar 

  38. Zaniolo, C., Analysis and design of relational schemata for database systems, Ph.D. Dissertation, Tech. Rep. UCLA-ENG-7669, UCLA, July 1976.

    Google Scholar 

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Authors and Affiliations

  1. IBM Research Laboratory, 95193, San Jose, California

    Ronald Fagin

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  1. Ronald Fagin
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Giorgio Ausiello Marco Protasi

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© 1983 Springer-Verlag Berlin Heidelberg

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Fagin, R. (1983). Acyclic database schemes (of various degrees): A painless introduction. In: Ausiello, G., Protasi, M. (eds) CAAP'83. CAAP 1983. Lecture Notes in Computer Science, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12727-5_3

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  • DOI: https://doi.org/10.1007/3-540-12727-5_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12727-7

  • Online ISBN: 978-3-540-38714-5

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