This Article 
 Bibliographic References 
 Add to: 
A Comparative Study of Various Nested Normal Forms
March/April 2002 (vol. 14 no. 2)
pp. 369-385

As object-relational databases (ORDBs) become popular in the industry, it is important for database designers to produce database schemes with good properties in these new kinds of databases. One distinguishing feature of an ORDB is that its tables may not be in first normal form. Hence, ORDBs may contain nested relations along with other collection types. To help the design process of an ORDB, several normal forms for nested relations have recently been defined, and some of them are called nested normal forms. In this paper, we investigate four nested normal forms, which are NNF 20, NNF 21, NNF 23, and NNF 25, with respect to generalizing 4NF and BCNF, reducing redundant data values, and design flexibility. Another major contribution of this paper is that we provide an improved algorithm that generates nested relation schemes in NNF 2 from an $ database scheme, which is the most general type of acyclic database schemes. After presenting the algorithm for NNF 20, the algorithms of all of the four nested normal forms and the nested database schemes that they generate are compared. We discovered that when the given set of MVDs is not conflict-free, NNF 20 is inferior to the other three nested normal forms in reducing redundant data values. However, in all of the other cases considered in this paper, NNF 20 is at least as good as all of the other three nested normal forms.

[1] C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, “On the Desirability of Acyclic Database Schemes,” J. ACM, vol. 30, pp. 479-513, 1983.
[2] C. Beeri and M. Kifer, “An Integrated Approach to Logical Design of Relational Database Schemes,” ACM Trans. Database Systems, vol. 11, no. 2, pp. 134–158, June 1986.
[3] G. Booch, J. Rumbaugh, and I. Jacobson, The Unified Modeling Language User Guide. Addison Wesley, 1999.
[4] M.J. Carey, N.M. Mattos, and A.K. Nori, “Object-Relational Database Systems: Principles, Products, and Challenges (Tutorial),” Proc. 1997 ACM SIGMOD Int'l Conf. Management of Data, p. 502, May 1997.
[5] A. Eisenberg and J. Melton,"SQL:1999, Formerly Known as SQL3," ACM SIGMOD Record, vol. 28, no. 1, Mar. 1999, pp. 131-138.
[6] R. Elmasri and S. Navathe, Fundamentals of Database Systems, third ed. Reading, Mass.: Addison-Wesley, 2000.
[7] R. Fagin, "Multivalued Dependencies and a New Normal Form for Relational Databases," ACM Trans. Database Systems, vol. 2, no. 3, pp. 262-278, Sept. 1977.
[8] R. Fagin, “Degrees of Acyclicity for Hypergraphs and Relational Database Schemes,” J. ACM, vol. 30, no. 3, pp. 514–550, July 1983.
[9] R. Fagin, A.O. Mendelzon, and J.D. Ullman, “A Simplified Universal Relation Assumption and Its Properties,” ACM Trans. Database Systems, vol. 7, no. 3, pp. 343–360, Sept. 1982.
[10] P.C. Fischer, L.V. Saxton, S.J. Thomas, and D. Van Gucht, “Interactions Between Dependencies and Nested Relational Structures,” J. Computer and System Sciences, vol. 31, no. 3, pp. 343–354, Dec. 1985.
[11] N. Goodman, O. Shmueli, and Y.C. Tay, “GYO Reductions, Canonical Connections, Tree and Cyclic Schemas and Tree Projections,” Proc. Second ACM SIGACT-SIGMOD Symp. Principles of Database Systems, pp. 267–278, Mar. 1983.
[12] M.H. Graham and M. Yannakakis, “Independent Database Schemas,” J. Computer and System Sciences, vol. 28, no. 1, pp. 121–141, 1984.
[13] H. Ishikawa et al., "The Design and Implementation of an Object-Oriented Multimedia Knowledge Base Management System," ACM Trans. Database Syst., vol. 18, no. 1, pp. 1-50, March 1993.
[14] ISO Database Language SQL—Part 2: Foundation (ISO/IEC 9075-2). Int'l Organization for Standardization, 1998.
[15] W. Kim, “Bringing Object/Relational Down to Earth,” Database Programming and Design, vol. 10, no. 7, pp. 26–35, July 1997.
[16] T.W. Ling and L.L. Yan, “NF-NR: A Practical Normal form for Nested Relations,” J. Systems Integration, vol. 4, pp. 309–340, 1994.
[17] D. Maier, The Theory of Relational Databases. Rockville, Md.: Computer Science Press, 1983.
[18] W.Y. Mok and D.W. Embley, “Transforming Conceptual Models to Object-Oriented Database Designs: Practicalities, Properties, and Peculiarities,” Conceptual Modeling—ER '96, pp. 309–324, Oct. 1996.
[19] W.Y. Mok and D.W. Embley, “Using NNF to Transform Conceptual Data Models to Object-Oriented Database Designs,” Data and Knowledge Eng., vol. 24, no. 3, pp. 313–336, Jan. 1998.
[20] W.Y. Mok, Y.K. Ng, and D.W. Embley, “A Normal Form for Precisely Characterizing Redundancy in Nested Relations,” ACM Trans. Database Systems, vol. 21, no. 1, pp. 77–106, Mar. 1996.
[21] Z. M. ${\rm Ozsoyo{\mathord{\buildrel{\lower.5pt\hbox{$\scriptscriptstyle\smile$}}\over {\rm g}}}lu}$ and L.-Y. Yuan, "A New Normal Form for Nested Relations," ACM Trans. Database Systems, vol. 12, no. 1, pp. 111-136, Mar. 1987.
[22] Z.M. Ozsoyoglu and L.Y. Yuan, “Reduced MVDs and Minimal Covers,” ACM Trans. Database Systems, vol. 12, no. 3, pp. 377–394, Sept. 1987.
[23] Z.M. Ozsoyoglu and L.Y. Yuan, “On the Normalization in Nested Relational Databases,” Lecture Notes in Computer Science, pp. 243–271, 1989.
[24] R. Ramakrishnan, Database Management Systems, McGraw-Hill, 1997.
[25] M.A. Roth and H.F. Korth, “The Design of$\neg$1nf Relational Databases into Nested Normal Form,” Proc. 1987 ACM SIGMOD Int'l Conf. Management of Data, pp. 143–159, May 1987.
[26] M.A. Roth, H.F. Korth, and A. Silberschatz, “Extended Algebra and Calculus for Nested Relational Databases,” ACM Trans. Database Systems, vol. 13, no. 4, pp. 389–417, Dec. 1988.
[27] M. Stonebraker, P. Brown, and D. Moore, Object-Relational DBMSs: Tracking the Next Great Wave, second ed. San Francisco: Morgan Kaufmann Publishers, 1999.
[28] E. Sciore, “Real-World MVD's,” Proc. 1981 ACM SIGMOD Int'l Conf. Management of Data, pp. 121–132, Apr. 1981.
[29] A. Silberschatz, H.F. Kort, and S. Sudarshan, Database System Concepts. McGraw-Hill, third ed., 1999.
[30] Z. Tari, J. Stokes, and S. Spaccapietra, “Object Normal Forms and Dependency Constraints for Object-Oriented Schemata,” ACM Trans. Database Systems, vol. 22, no. 4, pp. 513–569, Dec. 1997.
[31] S. Urman, Oracle8 PL/SQL Programming. Berkeley, Calif.: Osborne/McGraw-Hill, 1997.
[32] L.Y. Yuan and Z.M. Ozsoyoglu, “Design of Desirable Relational Database Schemes,” J. Computer and System Sciences, vol. 45, no. 3, pp. 435–470, Dec. 1992.
[33] L.Y. Yuan and Z.M. Ozsoyoglu, “Unifying Functional and Multivalued Dependencies for Relational Database Design,” Information Sciences, vol. 59, pp. 189–211, 1992.

Index Terms:
object-relational database management systems, object-relational databases, SQL:1999, nested relation schemes, nested relations, nested database schemes, nested databases, nested normal forms, conflict-free sets of MVDs, acyclic database schemes, nested database design, data redundancy, design flexibility, algorithms
W.Y. Mok, "A Comparative Study of Various Nested Normal Forms," IEEE Transactions on Knowledge and Data Engineering, vol. 14, no. 2, pp. 369-385, March-April 2002, doi:10.1109/69.991722
Usage of this product signifies your acceptance of the Terms of Use.