Theoretical foundation of algebraic optimization utilizing unnormalized relations

  • Marc H. Scholl
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 243)

Abstract

Unnormalized (NF2) relations, not conforming to the first normal form condition (1NF) of the relational model have been proposed recently for a variety of new applications. In this paper we extend NF2 relational theory in a way that it becomes possible to use NF2 relations as storage structures for conventional 1NF relational database interfaces. Physical clustering of precomputed joins can be achieved this way without introducing redundancy. However, applying transformation rules to internal relations straightforwardly, will still yield unnecessary join operations. With the equivalence rules introduced here we prove that efficient algebraic optimization can be performed using standard (1NF) techniques. Particularly, all redundant joins can be properly removed.

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7. References

  1. [AB84]
    S. Abiteboul, N. Bidoit: Non First Normal Form Relations to Represent Hierarchically Organised Data, Proc. 3rd ACM PODS, Waterloo, Ontario, Canada, 1984Google Scholar
  2. [ABU79]
    A.V. Aho, C. Beeri, J.D. Ullman: The Theory of Joins in Relational Databases, ACM TODS, Vol. 4:3, 1979Google Scholar
  3. [ASU79]
    A.V. Aho, Y. Sagiv, J.D. Ullman: Equivalences Among Relational Expressions, SIAM Journ. of Computing, Vol. 8:2, 1979Google Scholar
  4. [Bi85]
    N. Bidoit: Efficient Evaluation of Queries Using Nested Relations, Techn. Report INRIA, 1985Google Scholar
  5. [BR84]
    W. Benn, B. Radig: Retrieval of Relational Structures for Image Sequence Analysis, Proc. 10th VLDB Conference, Singapore, 1984Google Scholar
  6. [BRS82]
    F. Bancilhon, P. Richard, M. Scholl: On Line Processing of Compacted Relations, Proc. 8th VLDB Conference, Mexico, 1982Google Scholar
  7. [DOPSSW85]
    U. Deppisch, V. Obermeit, H.-B. Paul, H.-J. Schek, M.H. Scholl, G. Weikum: The Storage Component of a Database Kernel System, Techn. Rep. DVSI-1985-T1, TU Darmstadt, Short German version in: Proc. GI Conf. on DBSs in Office, Technical and Scientific Applications, Karlsruhe, 1985, IFB 94, Springer, german title: Ein Subsystem zur stabilen Speicherung versionenbehafteter, hierarchisch strukturierter Tupel Google Scholar
  8. [DPS86]
    U. Deppisch, H.-B. Paul, H.-J. Schek: A Storage System for Complex Objects, Proc. Int'l Workshop on Object-Oriented Database Systems, Pacific Grove, CA, 1986Google Scholar
  9. [Fa77]
    R. Fagin: Mulitvalued Dependencies and a New Normal Form for Relational Databases, ACM TODS, Vol. 2:3, 1977Google Scholar
  10. [FG85]
    P.C. Fischer, D. van Gucht: Determining When a Structure is a Nested Relation, Proc. 11th VLDB Conference, Stockholm, 1985Google Scholar
  11. [FT83]
    P.C. Fischer, S.J. Thomas: Operators for Non-First-Normal-Form Relations, Proc. IEEE COMPSAC 1983Google Scholar
  12. [Gu85]
    D. van Gucht: Theory of Unnormalized Relational Structures, Ph. D. Thesis, also available as Techn. Rep. CS-85-07, Vanderbilt University, Nassville, TN, 1985Google Scholar
  13. [Ja85]
    G. Jaeschke: Recursive Algebra for Relations with Relation Valued Attributes, Techn. Rep. TR 85.03.002, IBM Heidelberg Scientific Centre, 1985Google Scholar
  14. [Ja86]
    G. Jaeschke: Algebraic Expressions for Higher Order Relational Databases, unpublished manuscriptGoogle Scholar
  15. [JS82]
    G. Jaeschke, H.-J. Schek: Remarks on the Algebra of Non-First-Normal-Form Relations, Proc. 1st ACM PODS, Los Angeles, 1982Google Scholar
  16. [Ma83]
    D. Maier: The Theory of Relational Databases, Pitman Publishing Ltd., London, 1983Google Scholar
  17. [MSW86]
    F. Maher, H.-J. Schek, W. Waterfeld: A Database Kernel System for Geoscientific Applications, to appear in: Proc. 2nd Int'l Symp. on Spatial Data Handling, Seattle, 1986Google Scholar
  18. [OY85]
    Z.M. Ozsoyoglu, L.Y. Yuan: A Normal Form for Nested Relations, Proc. 4th ACM PODS, 1985Google Scholar
  19. [RKS85a]
    M.A. Roth, H.F. Korth, A. Silberschatz: Extended Algebra and Calculus for ¬1NF Relational Databases, Techn. Rep. TR-84-36, Revised Version, University of Texas at Austin, 1985Google Scholar
  20. [RKS85b]
    M.A. Roth, H.F. Korth, A. Silberschatz: Null Values in ¬1NF Relational Databases, Techn. Rep. TR-85-32, University of Texas at Austin, 1985Google Scholar
  21. [Sche85]
    H.-J. Schek: Towards a Basic Relational NF 2 Algebra Processor, Proc. Int'l Conf. on FODO, Kyoto, 1985Google Scholar
  22. [Sche86]
    H.-J. Schek: Research Activities of the DVSI-Group 1983–1985, Techn. Rep. DVSI-1986-T2, TU Darmstadt, 1986Google Scholar
  23. [SLTC82]
    N.C. Shu, V.Y. Lum, F.C. Tung, C.L. Chang: Specification of Forms Processing and Business Procedures for Office Automation, IEEE TOSE, Vol. SE-8:5, 1982Google Scholar
  24. [SP82]
    H.-J. Schek, P. Pistor: Data Structures for an Integrated Database Management and Information Retrieval System, Proc. 8th VLDB Conference, Mexico, 1982Google Scholar
  25. [SR86]
    H.-J. Schek, U. Reimer: A Frame Representation Model and its Mapping to NF 2 Relations, submitted for publication, 1986Google Scholar
  26. [SS80]
    M. Schkolnik, P. Sorenson: Denormalization: A Performance Oriented Database Design Technique, Proc. AICA Conf., Bologna, Italy, 1980Google Scholar
  27. [SS81]
    M. Schkolnik, P. Sorenson: The Effects of Denormalization on Database Performance, Res. Rep. RJ3082 (38128), IBM Res. Lab. San Jose, Ca., 1981Google Scholar
  28. [SS83]
    H.-J. Schek, M.H. Scholl: Die NF 2-Relationenalgebra zur einheitlichen Manipulation externer, konzeptueller und interner Datenstrukturen, in: J.W. Schmidt (ed.): Sprachen für Datenbanken, IFB 72, Springer, 1983Google Scholar
  29. [SS84]
    H.-J. Schek, M.H. Scholl: The Relational Model with Relation-Valued Attributes, Techn. Rep. DVSI-1984-T1, TU Darmstadt, published in: Information Systems, Vol. 11:2, 1986Google Scholar
  30. [SW86]
    H.-J. Schek, G. Weikum: DASDBS: Concepts and Architecture of a Database System for Advanced Applications, Techn. Rep. DVSI-1986-T1, TU Darmstadt, 1986Google Scholar
  31. [V86]
    Verso, J. (pen name for the Verso team): Verso: A Database Machine Based on Non-First-Normal-Form Relations, INRIA Report, 1986Google Scholar
  32. [Ul82]
    J.D. Ullman: Principles of Database Systems (2nd ed.), Computer Science Press, Rockville, MD, 1982Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Marc H. Scholl
    • 1
  1. 1.Department of Computer ScienceTechnical University of DarmstadtDarmstadtWest Germany

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