Boyce-Codd NF Takahiko Saito Spring 2005 CS 157A

Purpose of Normalization To reduce the chances for anomalies to occur in a database. To reduce the chances for anomalies to occur in a database. normalization prevents the possible corruption of databases stemming from what are called "insertion anomalies," "deletion anomalies," and "update anomalies." normalization prevents the possible corruption of databases stemming from what are called "insertion anomalies," "deletion anomalies," and "update anomalies."

Insertion Anomaly A failure to place a new database entry into all the places in the database where that new entry needs to be stored. A failure to place a new database entry into all the places in the database where that new entry needs to be stored. In a properly normalized database, a new entry needs to be inserted into only one place in the database In a properly normalized database, a new entry needs to be inserted into only one place in the database

Deletion Anomaly A failure to remove an existing database entry when it is time to remove that entry. A failure to remove an existing database entry when it is time to remove that entry. In a properly normalized database, an old, to-be-gotten-rid-of entry needs to be deleted from only one place in the database In a properly normalized database, an old, to-be-gotten-rid-of entry needs to be deleted from only one place in the database

Update anomaly An update of a database involves modifications that may be additions, deletions, or both. Thus "update anomalies" can be either of the kinds of anomalies discussed above. An update of a database involves modifications that may be additions, deletions, or both. Thus "update anomalies" can be either of the kinds of anomalies discussed above.

1st Normal Form A table (relation) is in 1NF if A table (relation) is in 1NF if 1. There are no duplicated rows in the table. 2. Each cell is single-valued 3. Entries in a column are of the same kind.

2nd Normal Form A table is in 2NF if it is in 1NF and if all non-key attributes are fully dependent on each candidate key. A table is in 2NF if it is in 1NF and if all non-key attributes are fully dependent on each candidate key. A partial dependency occurs when a non- key attribute is dependent on only a part of the (composite) key A partial dependency occurs when a non- key attribute is dependent on only a part of the (composite) key

1NF but not 2NF Supplier (supplier#, status, city, part#, quantity) Supplier (supplier#, status, city, part#, quantity) –(supplier#, part#) -> quantity –supplier# -> status –supplier# -> city –city -> status => status and city are dependent on just part of the key, namely supplier#. => status and city are dependent on just part of the key, namely supplier#.

1NF but not 2NF (cont ’ d) Decomposition (into 2NF): Decomposition (into 2NF): –Supplier (supplier#, status, city) –Supplier_Part (supplier#, part#, quantity)

3rd Normal Form (3NF) A table is in 3NF if it is in 2NF and if it has no transitive dependencies. A table is in 3NF if it is in 2NF and if it has no transitive dependencies. Transitive dependency is a functional dependency between non-key attributes. Transitive dependency is a functional dependency between non-key attributes.

2NF but not 3NF Supplier (supplier#, status, city) Supplier (supplier#, status, city) –supplier# -> status –supplier# -> city –city -> status => Lacks mutual independence among non-key attributes.

2NF but not 3NF (cont ’ d) Decomposition (into 3NF): Decomposition (into 3NF): –SUPPLIER_CITY (supplier#, city) –CITY_STATUS (city, status)

Boyce-Codd NF A table is in BCNF if it is in 3NF and if every determinant is a candidate key. A table is in BCNF if it is in 3NF and if every determinant is a candidate key. the definition of 3NF does not deal with a relation that: the definition of 3NF does not deal with a relation that: –has multiple candidate keys, where –Those candidate keys are composite, and –the candidate keys overlap (i.e., have at least one common attribute)

3NF but not boyce-codd NF SUPPLIER_PART (supplier#, supplier_name, part#, quantity) SUPPLIER_PART (supplier#, supplier_name, part#, quantity) –Two candidate keys: (supplier#, part#) and (supplier_name, part#) (supplier#, part#) and (supplier_name, part#) –(supplier#, part#) -> quantity –(supplier#, part#) -> supplier_name –(supplier#, part#) -> quantity –(supplier#, part#) -> supplier# –supplier_name -> supplier# –supplier# -> supplier_name

Another example of boyce-codd NF titleyearlengthfilmType studioNam e starName Star Wars colorFoxFisher colorFoxHamill colorFoxFord Mighty Ducks colorDisneyEsteves Wayne ’ s World colorParamountCarvey colorParamountMeyers

Example (cont ’ d) {title, year, starName} as candidate key {title, year, starName} as candidate key title, year  length, filmType, studioName title, year  length, filmType, studioName The above FD (Functional Dependency) violates the BCNF condition because title and year do not determine the sixth attribute, starName The above FD (Functional Dependency) violates the BCNF condition because title and year do not determine the sixth attribute, starName

Example (cont ’ d) We solve this BCNF violation by decomposing relation Movies into We solve this BCNF violation by decomposing relation Movies into 1. The schema with all the attributes of the FD {title, year, length, filmType, studioName} 2. The schema with all attributes of Movies except the three that appear on the right of the FD {title, year, starName}

Summary of Boyce-Codd NF When there is more than one candidate key, a relational table may be in 3NF and anomalies may still result. When there is more than one candidate key, a relational table may be in 3NF and anomalies may still result. This occurs when there is a composite primary key, and there are two equally valid candidates to make up part of this composite primary key. If there is an attribute (one or more columns) on which any other attribute is fully dependent, and this attribute is NOT itself a candidate key, then the table is not in Boyce-Codd Normal form (BCNF). This occurs when there is a composite primary key, and there are two equally valid candidates to make up part of this composite primary key. If there is an attribute (one or more columns) on which any other attribute is fully dependent, and this attribute is NOT itself a candidate key, then the table is not in Boyce-Codd Normal form (BCNF). We fix this by breaking the table up into two tables, both in BCNF. We fix this by breaking the table up into two tables, both in BCNF.