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Norman Pendegraft (University of Idaho, USA)

Source Title: Handbook of Research on Innovations in Database Technologies and Applications: Current and Future Trends

Copyright: © 2009
|Pages: 6
DOI: 10.4018/978-1-60566-242-8.ch002

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TopAn entity relationship diagram (ERD) shows the cardinality of each entity in a relationship. In an ERD, minimum cardinalities can be either 0 or 1, and maximum cardinalities can be 1 or infinity. Bounded cardinality occurs when a relationship between entities has cardinality within a specified range. Problems displaying bounded cardinality might include team rosters that must have exactly 5, 9, 11, or some other number of players. Figure 1 illustrates how UML (unified modeling language) provides for modeling specified-range relationships in a class diagram (Dennis, Wixom, & Tegarden, 2005). ERD, as described by Chen (1976), does not, although there are extensions to the ERD model that do (Webre, 1981). The SQL-92 standard provides for such constraints, but many relational database management systems (RDBMSs) do not support these features, and consequently do not allow for easy implementation of such a constraint (Lewis, Bernstein, & Kifer, 2002).

Bounded cardinality presents some interesting problems. For example, Boufares and Kraïem (2001) point out that cardinality constraints may result in conflicts. Figure 2 illustrates one of their examples. In Figure 2, if we let *e _{i}* be the number of instances of entity E

These lead in turn to e1 > e2 and e2 > 2 e1. Clearly these allow only the solution e1 = e2 =0, that is, an empty database. Boufares and Bennaceur (2004) offer a mathematical programming technique to detect inconsistent constraints.

Specified Range: UML term used to describe bounded cardinality in class diagrams.

Relationship: An association between entities.

Multiset: A collection in which elements may occur more than once.

Relation: For sets A and B, a relation R is a subset of the Cartesian product AXB, that is, R ? {(a, b)/a ? A, b ? B}. The relation may be written R(a,b) indicating that (a,b) is in R.

Procedural Constraint Support: Implementation of a constraint on a database via a procedure.

Bounded Cardinality: A specific finite upper and/or lower bound on the cardinality of a relationship between entities.

Reflexive Relation: If R is a relation on A, then a in A implies R(a,a). Sometimes it is erroneously used as a synonym for a symmetric relation.

Symmetric Relation: If R is a relation on AXA, then R is symmetric if and only if R(a,b) implies R(b,a).

Declarative Constraint Support: The ability of a database engine to implement constraints as part of the definition of the schema.

Semantic Constraint: In contrast to a structural constraint, a constraint that does not place a limit on the database structure.

Cardinality: The number of instances of an entity associated with a relationship.

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