## A New Normal Form for Nested Relations (1987)

Venue: | ACM Transactions on Database Systems |

Citations: | 55 - 2 self |

### BibTeX

@ARTICLE{Ozsoyoglu87anew,

author = {Z. Meral Ozsoyoglu and Li-yan Yuan},

title = {A New Normal Form for Nested Relations},

journal = {ACM Transactions on Database Systems},

year = {1987},

volume = {12},

pages = {111--136}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider nested relations whose schemes are structured as trees, called scheme trees, and introduce a normal form for such relations, called the nested normal form. Given a set of attributes U, and a set of multivalued dependencies (MVDs) M over these attributes, we present an algorithm to obtain a nested normal form decomposition of U with respect to M. Such a decomposition has several desirable properties, such as explicitly representing a set of full and embedded MVDs implied by M, and being a faithful and nonredundant representation of U. Moreover, if the given set of MVDs is conflict free, then the nested normal form decomposition is also dependency preserving. Finally, we show that if M is conflict free, then the set of root-to-leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition [Fa, L2] of U with respect to M. 1. Introduction A relational database [Co] is a collection of relations where each relation is at least in First ...

### Citations

459 |
The Theory of Relational Databases
- Maier
- 1983
(Show Context)
Citation Context ...ion to being a database scheme for nested relations, an NSF decomposition F has several desirable properties. First, F represents a set of full and embedded MVDs implied by M. Second, F is a faithful =-=[Ma]-=-, and a nonredundant (to be explained later) representation of U. Finally, if M is conflict free then F is a dependency preserving decomposition, i.e. MVDs represented by F is equivalent to M. Moreove... |

282 |
Principle of Database Systems
- Ullman
- 1982
(Show Context)
Citation Context ...r, the set of keys for N is unique since M - is the set of all reduced MVDs in M + = N + . Given a set M of MVDs, and a set X of attributes, DEP(X) denotes the dependency basis of X with respect to M =-=[Ul]. Elements of DE-=-P(X) are called dependents of X. Let RDEP(X) = {W �� X����W is reduced}. Obviously, RDEP(X)��DEP(X). Elements of RDEP(X) are called reduced dependents of X. By definition, a set of att... |

176 |
On the desirability of acyclic database schemes
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- 1983
(Show Context)
Citation Context ...COURSE, SECTION, GRADER)} is the unique 4NF decomposition [Fa] of U with respect to M, which is also in Split-Free Normal Form (SFNF) [BK2]. (Note that M in Example 1.1 is a conflict free set of MVDs =-=[L2, BFMY]-=-.) Given U and a set M of MVDs, we present a decomposition of U into a set of NNF relations (Section 4). Since the scheme of an NNF relation is a normal scheme tree, such a decomposition F={T 1 , ...,... |

130 | Multivalued dependencies and a new normal form for relational databases
- FAGIN
- 1977
(Show Context)
Citation Context ...so dependency preserving. Finally, we show that if M is conflict free, then the set of root-to-leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition =-=[Fa, L2]-=- of U with respect to M. 1. Introduction A relational database [Co] is a collection of relations where each relation is at least in First Normal Form (1NF), i.e., tuple components of a relation are at... |

111 |
Hans-Jörg Schek: Remarks on the algebra of non first normal form relations
- Jaeschke
- 1982
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Citation Context ...a normal form called Partitioned Normal Form for nested relations [RKS]. Recently, several researchers have reported query languages for non-first normal form relational databases. Jaeschke and Schek =-=[JS]-=- extended relational algebra by nest and unnest operators over single attributes to obtain nested relations from normalized relations and vice versa. Fischer and Thomas [FT] study operators for non-fi... |

73 |
Extending relational algebra and relational calculus with set-valued attributes and aggregate functions
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- 1987
(Show Context)
Citation Context ... for such relations by aggregation operators. A relational calculus for set valued relations with aggregate functions is given, and its equivalence to the corresponding relational algebra is shown in =-=[OzOM]-=-. A relational calculus for non-first normal form relations is given by Roth, Korth and Silberschatz [RKS], who also define a basic relational algebra for non-first normal form relations, and show its... |

47 | On the equivalence of database models - Lien - 1982 |

46 |
A sophisticate’s introduction to database normalization theory
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- 1978
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Citation Context ...ional calculus. In this paper, we introduce a normal form for nested relations, called the nested normal form (NNF). One of the objectives of NNF; as in previous normal forms, is to reduce redundancy =-=[BBG]-=-. Unlike flat normalized relations (such as 3NF, BCNF, 4NF, etc.), a nested relation has a nesting structure of its attributes which imply some semantic connections among attributes. Thus, a normal fo... |

17 |
Introduction to Systems Analysis and Design
- Hawryszkiewycz
- 2001
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Citation Context ...eme tree will be given later (Section 4). We first give an example. Example 1.1. Consider a database about course offerings, which contains information about COURSEs offered for study in a university =-=[Ha]-=-. Each COURSE is offered in any number of SECTIONs, and the same TEXT is used for the same COURSE in all SECTIONs. Each SECTION consists of a set of class meetings on a number of DAYs, and has a set o... |

12 |
E.: Hierarchical Schemata for Relational Databases
- Lien
- 1981
(Show Context)
Citation Context ...bove objectives, and then give a decomposition algorithm to obtain a NNF database scheme for U with respect to the given set of dependencies. For convenience, we consider FDs as MVDs, similar to Lien =-=[L1]-=-, i.e., we consider MVD counterparts of FDs. Informally, a relation is in NNF if it is structured in the form of a tree, called the normal scheme tree. Vertices of a normal scheme tree are pairwise di... |

11 |
A Relational Model for Large Shared
- Codd
- 1970
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Citation Context ...then the set of root-to-leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition [Fa, L2] of U with respect to M. 1. Introduction A relational database =-=[Co]-=- is a collection of relations where each relation is at least in First Normal Form (1NF), i.e., tuple components of a relation are atomic (nondecomposable) values. However, for non-business database a... |

11 |
Real world MVD's
- Sciore
- 1981
(Show Context)
Citation Context ...this example, D is a dependent of both A and B. However, B����D is derived from B����A and A����D by transitivity. M - {A����BC �� D} ���� B����D. T=-=hus, D is an essential dependent of A but not B. In [Sc]-=-, a different definition for essential dependents is given. With respect to that definition, D in the above example is an essential dependent of both A and B. Thus, the definition in [Sc] does not dis... |

7 |
An extension of relational algebra for summary tables
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- 1983
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Citation Context ...e general setting. Abiteboul and Bideout [AB] describe the use of non-first normal form relations in the VERSO machine [Ba], and give algebraic operators and their properties. Ozsoyoglu and Ozsoyoglu =-=[OO]-=- consider operators similar to that of [JS], for set valued relations (i.e., relations with at most one level of __________________ * This research is supported in part by the NSF under Grant No-83066... |

6 |
Unifying functional and multivalued dependencies for relational database design
- Yuan, Ozsoyoglu
- 1986
(Show Context)
Citation Context ...However, any flat relation is also in PNF trivially, since in this case the scheme tree consists of a single node whose label is the set of all attributes of the relation. Recently, we have presented =-=[YO]-=- a unifying approach to incorporate FD's and MVD's into database design. Utilizing these results will improve the design of nested normal form database schemes, but is beyond the scope of this paper. ... |

5 |
Operators for Non-First-Normal Form Relations
- Fisher, Thomas
- 1983
(Show Context)
Citation Context ...abases. Jaeschke and Schek [JS] extended relational algebra by nest and unnest operators over single attributes to obtain nested relations from normalized relations and vice versa. Fischer and Thomas =-=[FT]-=- study operators for non-first normal form relations in a more general setting. Abiteboul and Bideout [AB] describe the use of non-first normal form relations in the VERSO machine [Ba], and give algeb... |

5 | Reduced mvds and minimal covers
- Ozsoyoglu, Yuan
- 1987
(Show Context)
Citation Context ...the set of all reduced MVDs implied by M, i.e., M - = {X����W �� X����W is a reduced MVD in M + }. Then, from the following lemma and the definition of reduced MVDs, M - is a cover=-= of M + . Lemma 2.1 [OY]. Let X����W be a nonred-=-uced MVD in M + . Then there exists a reduced MVD X����W in M + such that X �� X and XW �� XW, and if W �� DEP(X) then W = HW, where H �� (X - X). Definition 2.2. A set of MVDs... |

4 |
Elimination of Intersection Anomalies from Database Schemes
- Beeri, Kifer
- 1986
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Citation Context ... in T. In this case, MD(X, D(v), S(T)) is said to be a transitive dependency in S(T). Note that, if v is partial or transitive redundant in T with respect to X, then MD(X, D(v), S(T)) is a projection =-=[BK1] of a right-reduced MVD over-=- U, which is implied by M. Example 4.1 Let U = ABCDEFGH and M = {A ���� B, AC ���� EFG, BE ���� AF �� D}. Keys of M are A, AC, BE, AE, AEC and BEC. Consider the following s... |

2 |
On the Design of Relational Database Schemata
- Zaniola, Melknoff
- 1981
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Citation Context ...over of reduced MVDs is to eliminate the - 6 - redundancies of nonreduced MVDs. It should be noted that, minimal covers of left- and right-reduced (but not necessarily reduced) MVDs are considered in =-=[ZM]-=-, and covers of right-reduced MVDs are considered in [BFMY]. As usual, we use LHS(M) to denote the set of left hand sides of the MVDs in a set M of MVDs. Definition 2.3. Let N be a set of MVDs, and M ... |

1 |
Non First Normal for Relations to Represent Hierarchically Organized
- Abiteboul, Bidoit
- 1984
(Show Context)
Citation Context ...butes to obtain nested relations from normalized relations and vice versa. Fischer and Thomas [FT] study operators for non-first normal form relations in a more general setting. Abiteboul and Bideout =-=[AB]-=- describe the use of non-first normal form relations in the VERSO machine [Ba], and give algebraic operators and their properties. Ozsoyoglu and Ozsoyoglu [OO] consider operators similar to that of [J... |

1 |
Verso: A Relational Back End Data Base
- Bancilhon
- 1982
(Show Context)
Citation Context ...cher and Thomas [FT] study operators for non-first normal form relations in a more general setting. Abiteboul and Bideout [AB] describe the use of non-first normal form relations in the VERSO machine =-=[Ba]-=-, and give algebraic operators and their properties. Ozsoyoglu and Ozsoyoglu [OO] consider operators similar to that of [JS], for set valued relations (i.e., relations with at most one level of ______... |

1 |
A Complete Axiomatization for FDs and MVDs
- Beeri, Fagin, et al.
- 1977
(Show Context)
Citation Context ...���(U - XY). M2:(reflexivity) If Y�� X then X����Y. M3:(augmentation) If X����Y and Z �� W then XW����YZ. M4:(transitivity) If X����Y and Y����Z t=-=hen X����Z - Y. The inference rules M1 - M4 are shown [BFH]-=- to be sound and complete for MVDs. Since we consider only MVDs, we use the inference rule FM0 to obtain MVD counterparts of FDs as in [L1]. For a set M of MVDs, M + denotes the closure of M, i.e. the... |

1 |
Comprehensive Approach to the Design
- Beeri, Kifer
- 1984
(Show Context)
Citation Context ... path set of T R , i.e. {(COURSE, TEXT), (COURSE, SECTION, DAY), (COURSE, SECTION, GRADER)} is the unique 4NF decomposition [Fa] of U with respect to M, which is also in Split-Free Normal Form (SFNF) =-=[BK2]-=-. (Note that M in Example 1.1 is a conflict free set of MVDs [L2, BFMY].) Given U and a set M of MVDs, we present a decomposition of U into a set of NNF relations (Section 4). Since the scheme of an N... |

1 | Theory of Non-First-Normal Form Relational Databases - Roth, Korth, et al. - 1984 |