Normalisation The theory of Relational Database Design

Introduction Normalisation is a theory for designing relational schema that “make sense” and work well. Well-normalised tables avoid redundancy and thereby reduce inconsistencies. Redundancy is unnecessary duplication. In well-normalised DBs semantic dependencies are maintained by primary key uniqueness.

Goals of Normalisation Eliminate certain kinds of redundancy avoid certain update anomalies good reresentation of real world simplify enforcement of DB integrity

Update anomalies Undesirable side-effects that occur when performaing insertion, modification or deletion operations on badly designed relational DBs. SSN Name J Smith M Burke A Dolan K Doyle O O’Neill R McKay Dept DeptMgr Representing Department info in the Employee table causes problems. Dept Name …...

Sample anomalies Modification - –when the manager of a dept changes we have to change many values. –If we are not careful the DB will contain inconsistencies. –There is no easy way to get the DB to ensure that a department has only one manager and only one name.

Anomalies continued Deletion - –if O O’Neill leaves we delete his tuple and lose the fact that there is a department 3 the name of dept 3 who is the manager of dept. 3 Insertion –how would we create a new department before any employees are assigned to it ?

Better design Separate entities are represented in separate tables. SSN Name J Smith M Burke A Dolan K Doyle O O’Neill R McKay Dept Dept DeptMgr Dept Name …... Note that mapping from an ER model following the steps given will give a well-normalised DB.

Boyce-Codd Normal Form After a lot of other approaches Boyce and Codd noticed a simple rule for ensuring tables are well-normalised. Tables which obey the rule are in BCNF (Boyce Codd Normal Form). BCNF rule: Every determinant in a table must be a candidate key for that table.

Determinants A is a determinant of B if each value of A has precisely one (possibly null) associated value of B. Said another way - A is a determinant of B if and only if whenever two tuples agree on their A value they agree on their B value. AB

Determinants Note that determinancy depends on semantics of data –cannot be decided from individual table occurences. Alternative terminology –if A (functionally) determines B then –B is (functionally) dependent on A

Example determinants SSN determines employee name SSN determines employee department Dept. No. determines Dept. Name Dept. Name determines Dept. No. –assuming Dept. names are also unique Emp. Name does not determine Emp. Dept –two John Smiths could be in difft. Depts. Emp. Name does not determine SSN.

Determinancy Diagram SSN Name Department Dept. Name Dept. Mgr In general key attributes of an entity determine all the single-valued attributes of the entity.

Composite Determinants (SSN, Project#) together determine the hours that the employee works on the project. Suppose packsize of a part depends on the supplier. SSN Project# hours PName Name S# P# packsize PName

Superfluous Attrbiutes Superfluous attributes –If SSN determines name, so does (SSN, Dept) and (SSN, Dept, salary), etc. –Always remove superfluous attributes from determinants.

Transitive Dependencies SSN actually determines DeptMgr but only because –SSN determines DeptNo and –DeptNo determines DeptMgr. Be careful to remove transitive dependencies. –They mess up normalisation. SSN DeptNo Dept. Mgr

Candidate keys candidate key = any attribute or set of attributes which will be unique for a table (set of attributes). –As well as the primary key there may be other candidate keys. –E.g. DNUMBER and DNAME are both candidate keys for the Department table. Key = row identifier Candidate key = candidate identifier

Finding candidate keys Every key is by definition a determinant of all other attributes in a relation. –So in a diagram, any attribute (or composite) from which all other attributes are reachable is a candidate key. SSN Project# hours PName Name (SSN, Project#) is a (composite) candidate key for a table containing these five attributes.

What are the candidate keys ? D E F GHJ K L M N PQ R S T U student subject teacher V W X Y A Z C B B D F E G H

Problems occur when... Redundancy and anomalies occur when there are determinants which are not candidate keys. SSN Name DeptNo Dept. Name Dept. Mgr SSN is the only key for a table containing these attributes –all attributes are reachable from SSN. SSN, DeptNo and DeptName are determinants –they have arrows coming out of them.

BCNF rule In well-normalised relations (Boyce-Codd normal form) every determinant is a candidate key. SSN Name DeptNo Dept. Name Dept. Mgr DeptNo The employee/dept table decomposed to BCNF. Note that both DeptNo and DeptName are candidate keys of the second table.

Transformation to BCNF Create new tables such that each non-key determinant is a candidate key in a new table. The new table contains the attributes which are directly determined by the new candidate key. V W X Y A Z C B V X V W Y V W A Z A C B BCNF tables : (V, X) (A, B, C) (V, W, Z, A) (V, W, Y)

Other Normal Forms First NF - no multi-valued attributes –all relational DBs are 1NF 2NF - every non-key attribute is fully dependent on the primary key 3NF - eliminate functional dependencies between non-key attributes –all dependencies can then be enforced by uniqueness of keys. GHJ Table is in 2NF but not 3NF

BCNF vs. 3NF BCNF goes further than 3NF, some say too far. A 3NF table that has no overlapping composite keys is in BCNF. student subject teacher 3NF, not BCNF keys: (student, subject) (student, teacher) teacher is a determinant studentteacher subjectteacher BCNF but tables are not independent A teacher teaches only one subject. For a given subject a given student has only one teacher.

4NF : Multi-valued dependencies If a course can have multiple teachers and multiple texts, blind mapping to 1NF will give Subject Physics Maths Teacher Green Brown Green Brown Green Text Basic Mechanis Basic Mechanics Principles of Optics Basic Mechanics Vector Analysis Trigonometry which clearly has redundancy.

Fully-normalised BCNF relations are well-normalised Fully-normalised relations are those with no multi-valued dependencies (4NF) and no join dependencies (5NF).