Intro to Relational Model.pdf

Chapter 2: Intro to Relational Model Database System Concepts, 7th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use  Outline  Structure of Relational Databases ...

Chapter 2: Intro to Relational Model Database System Concepts, 7th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use  Outline  Structure of Relational Databases  Database Schema  Keys  Schema Diagrams  Relational Query Languages  The Relational Algebra Database System Concepts - 7th Edition 2.2 ©Silberschatz, Korth and Sudarshan  Example of a Instructor Relation attributes (or columns) tuples (or rows) Database System Concepts - 7th Edition 2.3 ©Silberschatz, Korth and Sudarshan  Attribute  The set of allowed values for each attribute is called the domain of the attribute  Attribute values are (normally) required to be atomic; that is, indivisible  The special value null is a member of every domain. Indicated that the value is “unknown”  The null value causes complications in the definition of many operations Database System Concepts - 7th Edition 2.4 ©Silberschatz, Korth and Sudarshan  Relations are Unordered  Order of tuples is irrelevant (tuples may be stored in an arbitrary order)  Example: instructor relation with unordered tuples Database System Concepts - 7th Edition 2.5 ©Silberschatz, Korth and Sudarshan  Database Schema  Database schema -- is the logical structure of the database.  Database instance -- is a snapshot of the data in the database at a given instant in time.  Example: schema: instructor (ID, name, dept_name, salary) Instance: Database System Concepts - 7th Edition 2.6 ©Silberschatz, Korth and Sudarshan  Keys  Let K ⊆ R  K is a superkey of R if values for K are sufficient to identify a unique tuple of each possible relation r(R) Example: {ID} and {ID,name} are both superkeys of instructor.  Superkey K is a candidate key if K is minimal Example: {ID} is a candidate key for Instructor  One of the candidate keys is selected to be the primary key. which one?  Foreign key constraint: Value in one relation must appear in another Referencing relation Referenced relation Example – dept_name in instructor is a foreign key from instructor referencing department Database System Concepts - 7th Edition 2.7 ©Silberschatz, Korth and Sudarshan  Schema Diagram for University Database Database System Concepts - 7th Edition 2.8 ©Silberschatz, Korth and Sudarshan  Relational Query Languages  Procedural versus non-procedural, or declarative  “Pure” languages: Relational algebra Tuple relational calculus Domain relational calculus  The above 3 pure languages are equivalent in computing power  We will concentrate in this chapter on relational algebra Not turning-machine equivalent Consists of 6 basic operations Database System Concepts - 7th Edition 2.9 ©Silberschatz, Korth and Sudarshan  Relational Algebra  A procedural language consisting of a set of operations that take one or two relations as input and produce a new relation as their result.  Six basic operators select: σ project: ∏ union: ∪ set difference: – Cartesian product: x rename: ρ Database System Concepts - 7th Edition 2.10 ©Silberschatz, Korth and Sudarshan  Select Operation  The select operation selects tuples that satisfy a given predicate.  Notation: σ p(r)  p is called the selection predicate  Example: select those tuples of the instructor relation where the instructor is in the “Physics” department. Query σ dept_name=“Physics” (instructor) Result Database System Concepts - 7th Edition 2.11 ©Silberschatz, Korth and Sudarshan  Select Operation (Cont.)  We allow comparisons using =, ≠, >, ≥. 90,000 (instructor)  Then select predicate may include comparisons between two attributes. Example, find all departments whose name is the same as their building name: σ dept_name=building (department) Database System Concepts - 7th Edition 2.12 ©Silberschatz, Korth and Sudarshan  Project Operation  A unary operation that returns its argument relation, with certain attributes left out.  Notation: ∏ A1,A2,A3 ….Ak (r) where A1, A2 are attribute names and r is a relation name.  The result is defined as the relation of k columns obtained by erasing the columns that are not listed  Duplicate rows removed from result, since relations are sets Database System Concepts - 7th Edition 2.13 ©Silberschatz, Korth and Sudarshan  Project Operation (Cont.)  Example: eliminate the dept_name attribute of instructor  Query: ∏ID, name, salary (instructor)  Result: Database System Concepts - 7th Edition 2.14 ©Silberschatz, Korth and Sudarshan  Composition of Relational Operations  The result of a relational-algebra operation is relation and therefore of relational-algebra operations can be composed together into a relational-algebra expression.  Consider the query -- Find the names of all instructors in the Physics department. ∏name(σ dept_name =“Physics” (instructor))  Instead of giving the name of a relation as the argument of the projection operation, we give an expression that evaluates to a relation. Database System Concepts - 7th Edition 2.15 ©Silberschatz, Korth and Sudarshan  Cartesian-Product Operation  The Cartesian-product operation (denoted by X) allows us to combine information from any two relations.  Example: the Cartesian product of the relations instructor and teaches is written as: instructor X teaches  We construct a tuple of the result out of each possible pair of tuples: one from the instructor relation and one from the teaches relation (see next slide)  Since the instructor ID appears in both relations we distinguish between these attribute by attaching to the attribute the name of the relation from which the attribute originally came. instructor.ID teaches.ID Database System Concepts - 7th Edition 2.16 ©Silberschatz, Korth and Sudarshan  The instructor X teaches table Database System Concepts - 7th Edition 2.17 ©Silberschatz, Korth and Sudarshan  Join Operation  The Cartesian-Product instructor X teaches associates every tuple of instructor with every tuple of teaches. Most of the resulting rows have information about instructors who did NOT teach a particular course.  To get only those tuples of “instructor X teaches “ that pertain to instructors and the courses that they taught, we write: σ instructor.id = teaches.id (instructor x teaches )) We get only those tuples of “instructor X teaches” that pertain to instructors and the courses that they taught.  The result of this expression, shown in the next slide Database System Concepts - 7th Edition 2.18 ©Silberschatz, Korth and Sudarshan  Join Operation (Cont.)  The table corresponding to: σ instructor.id = teaches.id (instructor x teaches)) Database System Concepts - 7th Edition 2.19 ©Silberschatz, Korth and Sudarshan  Join Operation (Cont.)  The join operation allows us to combine a select operation and a Cartesian-Product operation into a single operation.  Consider relations r (R) and s (S)  Let “theta” be a predicate on attributes in the schema R “union” S. The join operation r ⋈𝜃𝜃 s is defined as follows: 𝑟𝑟 ⋈𝜃𝜃 𝑠𝑠 = 𝜎𝜎𝜃𝜃 (𝑟𝑟 × 𝑠𝑠)  Thus σ instructor.id = teaches.id (instructor x teaches ))  Can equivalently be written as instructor ⋈ Instructor.id = teaches.id teaches. Database System Concepts - 7th Edition 2.20 ©Silberschatz, Korth and Sudarshan  Union Operation  The union operation allows us to combine two relations  Notation: r ∪ s  For r ∪ s to be valid. 1. r, s must have the same arity (same number of attributes) 2. The attribute domains must be compatible (example: 2nd column of r deals with the same type of values as does the 2nd column of s)  Example: to find all courses taught in the Fall 2017 semester, or in the Spring 2018 semester, or in both ∏course_id (σ semester=“Fall” Λ year=2017 (section)) ∪ ∏course_id (σ semester=“Spring” Λ year=2018 (section)) Database System Concepts - 7th Edition 2.21 ©Silberschatz, Korth and Sudarshan  Union Operation (Cont.)  Result of: ∏course_id (σ semester=“Fall” Λ year=2017 (section)) ∪ ∏course_id (σ semester=“Spring” Λ year=2018 (section)) Database System Concepts - 7th Edition 2.22 ©Silberschatz, Korth and Sudarshan  Set-Intersection Operation  The set-intersection operation allows us to find tuples that are in both the input relations.  Notation: r ∩ s  Assume: r, s have the same arity attributes of r and s are compatible  Example: Find the set of all courses taught in both the Fall 2017 and the Spring 2018 semesters. ∏course_id (σ semester=“Fall” Λ year=2017 (section)) ∩ ∏course_id (σ semester=“Spring” Λ year=2018 (section)) Result Database System Concepts - 7th Edition 2.23 ©Silberschatz, Korth and Sudarshan  Set Difference Operation  The set-difference operation allows us to find tuples that are in one relation but are not in another.  Notation r – s  Set differences must be taken between compatible relations. r and s must have the same arity attribute domains of r and s must be compatible  Example: to find all courses taught in the Fall 2017 semester, but not in the Spring 2018 semester ∏course_id (σ semester=“Fall” Λ year=2017 (section)) − ∏course_id (σ semester=“Spring” Λ year=2018 (section)) Database System Concepts - 7th Edition 2.24 ©Silberschatz, Korth and Sudarshan  The Assignment Operation  It is convenient at times to write a relational-algebra expression by assigning parts of it to temporary relation variables.  The assignment operation is denoted by ← and works like assignment in a programming language.  Example: Find all instructor in the “Physics” and Music department. Physics ← σ dept_name=“Physics” (instructor) Music ← σ dept_name=“Music” (instructor) Physics ∪ Music  With the assignment operation, a query can be written as a sequential program consisting of a series of assignments followed by an expression whose value is displayed as the result of the query. Database System Concepts - 7th Edition 2.25 ©Silberschatz, Korth and Sudarshan  The Rename Operation  The results of relational-algebra expressions do not have a name that we can use to refer to them. The rename operator, ρ , is provided for that purpose  The expression: ρx (E) returns the result of expression E under the name x  Another form of the rename operation: ρx(A1,A2,.. An) (E) Database System Concepts - 7th Edition 2.26 ©Silberschatz, Korth and Sudarshan  Equivalent Queries  There is more than one way to write a query in relational algebra.  Example: Find information about courses taught by instructors in the Physics department with salary greater than 90,000  Query 1 σ dept_name=“Physics” ∧ salary > 90,000 (instructor)  Query 2 σ dept_name=“Physics” (σ salary > 90.000 (instructor))  The two queries are not identical; they are, however, equivalent -- they give the same result on any database. Database System Concepts - 7th Edition 2.27 ©Silberschatz, Korth and Sudarshan  Equivalent Queries  There is more than one way to write a query in relational algebra.  Example: Find information about courses taught by instructors in the Physics department  Query 1 σdept_name=“Physics” (instructor ⋈ instructor.ID = teaches.ID teaches)  Query 2 (σdept_name=“Physics” (instructor)) ⋈ instructor.ID = teaches.ID teaches  The two queries are not identical; they are, however, equivalent -- they give the same result on any database. Database System Concepts - 7th Edition 2.28 ©Silberschatz, Korth and Sudarshan  End of Chapter 2 Database System Concepts - 7th Edition 2.29 ©Silberschatz, Korth and Sudarshan 

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