Normalization
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The document discusses algorithms for relational database schema design and decomposition. It covers topics like dependency preservation, lossless join properties, synthesizing relations in BCNF and 3NF, and dealing with null values. The key algorithms presented are for relational synthesis into 3NF while preserving dependencies, and relational decomposition into BCNF with lossless joins. Testing for lossless join properties and the potential "dangling tuple" problem with null values are also addressed.
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This document discusses relations and functions for class 12. It defines concepts like cartesian product, relations, domain and codomain, range, types of relations such as reflexive, symmetric, transitive and equivalence relations. It also defines functions, one-to-one and onto functions, bijective functions, composition of functions, and inverse functions. An example is provided to show that a given relation is reflexive but not symmetric or transitive. Another example shows a given function is one-to-one but not onto.
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This document discusses query languages and relational algebra operations. It introduces relational algebra as a procedural query language. The basic relational algebra operations are selection, projection, union, set difference, cartesian product, and rename. Examples are provided to illustrate each operation. Additional operations like join, outer join, division and aggregation are also discussed. The document concludes with a discussion of database modification operations like deletion, insertion and updating.
test
The document discusses relational database design and functional dependencies. It defines functional dependencies and provides examples. It describes different types of functional dependencies like trivial, non-trivial, and how functional dependencies relate to keys. It explains Armstrong's axioms for reasoning about functional dependencies and various properties and algorithms related to functional dependencies like closure of sets of attributes and functional dependencies.
structureformal1.ppt
This document provides an overview of different structures in formal methods and software engineering, including tuples, records, relations, tables, databases, pairs, binary relations, functions, and sequences. It discusses topics such as tuples associating elements in a fixed order, relations modeling tables and databases, pairs associating two components, functions associating a single item to each element in a set, and sequences being ordered collections. It also covers operators for these structures like projection, relation image, domain restriction, range restriction, composition, and inverse.
354 ch6
Relational algebra is a set of operations used to specify queries on relational databases. The basic operations include select, project, join, union, intersection, and cartesian product. A sequence of relational algebra operations forms a query that manipulates relations and returns a relation of results. Common uses of the operations include retrieving subsets of tuples, projecting columns, joining tables, and set operations to combine relations.
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Normalization
- 1. METU Department of Computer Eng Ceng 302 Introduction to DBMS Relational Database Design Algorithms by Pinar Senkul resources: mostly froom Elmasri, Navathe and other books
- 12. Properties of Relational Decompositions Lossless (nonadditive) join test for n -ary decompositions. (a) Case 1: Decomposition of EMP_PROJ into EMP_PROJ1 and EMP_LOCS fails test. (b) A decomposition of EMP_PROJ that has the lossless join property.
- 13. Properties of Relational Decompositions Lossless (nonadditive) join test for n -ary decompositions. (c) Case 2: Decomposition of EMP_PROJ into EMP, PROJECT, and WORKS_ON satisfies test.
- 17. Algorithms for Relational Database Schema Design Example: R={ssn,ename,bdate,address,dno,dname,dmgrssn} {ssn} {ename,bdate,address,dno} {dno } {dname,dmgrssn} R1 = {ssn,ename,bdate,address,dno} R2 = {dno,dname,dmgrssn}
- 19. Algorithms for Relational Database Schema Design Example: R={student, course, instructor} {student, course} {instructor} {instructor } {course} R1 = {student, instructor} R2 = {instructor, course}
- 20. Algorithms for Relational Database Schema Design Issues with null-value joins. (a) Some EMPLOYEE tuples have null for the join attribute DNUM.
- 21. Algorithms for Relational Database Schema Design Issues with null-value joins. (b) Result of applying NATURAL JOIN to the EMPLOYEE and DEPARTMENT relations. (c) Result of applying LEFT OUTER JOIN to EMPLOYEE and DEPARTMENT.
- 22. Algorithms for Relational Database Schema Design The “dangling tuple” problem.
- 23. Algorithms for Relational Database Schema Design The “dangling tuple” problem. (b) The relation EMPLOYEE_2 (includes DNUM attribute with null values). (c) The relation EMPLOYEE_3 (includes DNUM attribute but does not include tuples for which DNUM has null values).