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Chapter 3 Data Modeling Using the Entity-Relationship (ER) Model 3.4 Relationship Types, Relationship Sets, Roles, and Structural Constraints In Figure 3.8 there are several irnplicit relationships an-lol-rg the varrious entity types. In fact, whenever an attribute of one entity type refers to another entitv type, some relationship exists. For example, the attribute Manager of DEPARTMENT refers to an employee who manirges the department; the attribute Controlling-department oi PROJECT refers to the departn-rer.rt that controls the project; the attribute Supervisor of EMPLOYEE refers to another employee (the one who supervises this employee); the attribute Department of EMPLOYEE refers to the department for which the employee rvorks; and so or.r. In the ER moclel, these references should not be represented as attributes but as relationships, which are discussed in this section. The COMPANY databa-se scher.na will be refined in Section 3.6 to represent relationships explicitly. In the initial design of entity types, relationships are typically captured in the tbrm of attributes. As the design is retined, these attributes get converted into relationships between entity types. This section is organized as fbllows: Section 3.4.1 introduces the concepts of relationship types, relationship sets, and relationship instances. We define the concepts of relationship degree, role narnes, and recursive relationships in Section 3.4.2, and then we discuss structural constraints on relationships-such as cardinality ratios and existence dependencies-in Section 3.4.3. Section 3,4.4 shows how relationship types can also have attribr,rtes. 3.4.1 Relationship Types, Sets, and Instances A relationship type R an'rong n entity types E', E2, . . ., E,, defines a set of associations-or a relationship set-among entities from these entity types. As for the case of entity types and entity sets, a relationship type and its corresponding relationship set are customarily referred to by the same neme, R. Mathematically, the relationship set R is a set oI relationship instances r;, where each r, associates n individual entities (ep e1, .. ., c,,), and each entity e, in r; is a member of entity type E', I 3 j! n. Hence, a relationship type is a mathematical relation on E1, E2, . . ., Er; alternatively, it can be deflned as a subset of the Cartesian product E, x Erx . . . x E,,. Each of the entity types E1, E ., . . ., E,, is said to participate in the relationship type R; similarly, each of tl-re individual entities €D e,,. .., e,, is said to participate in the relationship instarnce r;= (ey, e., . . ., e,,). Informally, each relationship instance r; in R is an association of entities, where the association includes exactly one entity from each participating entity type. Each such rel:.rtionship instance r, represents the fact that the entities participating in r' are related in some way in the corresponding miniworld situation. For example, consider a relationship type WORKS-FOR between the two entity types EMPLOYEE and DEPARTMENT, rvhich associates each employee with the department for which the employee works. Each relationship instance in the relationship set WORKS-FOR associates one EMPLOYEE entity and one DEPARTMENT entity. Figure 3.9 illustrates this example, where each relationship instance r; is shown connected to the
pes. Jme oan rt of visor the The hips :d in into rela- -epts and atios rship ociar the rela- .', the indi- tlter- Each slm- Ilon- 'e the Fach .tnri nple, ]YEE rhich _FOR trates r the -3. EMPLOYEE €1 €3 €4 3.4 Relationship Types, Relationship Sets, Roles, and Structural Constraints 71 WORKS FOR DEPARTMENT :MPLOYEE and DEPARTMENT entities that participate in r,. In the miniworld repre- .crrted by Figure 3.9, employe€S s1, er, and eu work for department d,; employees el .rnd en work for department d,; and employees e. and e, work for department d.,. In ER diagrams, relationship types are displayed as diamond-shaped boxes, which rrc connected by straight lines to the rectangular boxes representing the participating entity types. The relationship name is displayed in the diamond-shaped box (see Irigure 3.2). 3.4.2 Relationship Degree, Role Names, and Recursive Relationships Degree of a Relationship Type. The degree of a relationship type is the number oi participating entity types. Hence, the WORKS FOR relationship is of degree two. .\ relationship type of degree two is called binary, and one of degree three is called ternary. An example of a ternary relationship is SUPPLY, shown in Figure 3.10, rvhere each relationship instance r, associates three entities-a supplier s, a part p, .ind a project j-whenever s supplies partP to project j. Relationships can generaliy be of any degree, but the ones most comrnon are binary relationships. Higherdegree relationships are generally more complex than binary relationships; we char- .rcterize them further in Section 3.9. Figure 3.9 Some 'nstarces in the WORKS_[OR relatror srip cet whirl' renre..enls r .elationship type WORKS_FOR between EMPLOYEE and DEPARTIVENT.
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