Question

Consider the following relation for published books: BOOK (Book_title, Authorname, Book_type, Listprice, Author_affil, Publisher) Author_affil refers to the affliation of author. Suppose the following dependencies exist: Book_title \(\rightarrow\) Publisher, Book_type Book_type \(\rightarrow\) Listprice Authorname \(\rightarrow\) Author-affil a. What normal form is the relation in? Explain your answer. b. Apply normalization until you cannot decompose the relations further. State the reasons behind each decomposition.

Short answer

The given relation is in Second Normal Form (2NF). It can be decomposed to two relations R1(Book_title, Publisher, Authorname, Author_affil) and R2(Book_type, Listprice) to reach Third Normal Form (3NF) and further to BCNF as there are no more dependencies that violate the BCNF condition.

Step-by-step solution

Analyzing the Dependencies

From the question, the functional dependencies are Book_title \(\rightarrow\) Publisher, Book_type, Book_type \(\rightarrow\) Listprice and Authorname \(\rightarrow\) Author_affil. To determine the normal form, check if these dependencies satisfy the conditions for 1NF, 2NF, 3NF and BCNF.

Determining the Normal Form

The relation is in 1NF because each attribute has atomic values. It's in 2NF because there are no partial dependencies (an attribute dependent on part of the primary key), assuming the primary key is Book_title. It's not in 3NF because there is a transitive dependency (Book_type \(\rightarrow\) Listprice and Book_title \(\rightarrow\) Book_type). Therefore, this relation is in 2NF.

Decomposing to 3NF

To remove the transitive dependency and achieve 3NF, decompose the relation into two: R1(Book_title, Publisher, Authorname, Author_affil) and R2(Book_type, Listprice). Now, in R1, Book_title \(\rightarrow\) Publisher, Authorname and in R2, Book_type \(\rightarrow\) Listprice, therefore these two relations are in 3NF. The reasons behind this decomposition is to remove the transitive dependency, maintain data integrity and reduce redundancy.

Decomposing to BCNF

The relations R1 and R2 are already in Boyce-Codd Normal Form (BCNF) because for each relation, for every one of its dependencies X \(\rightarrow\) Y, X is a super key. This means we cannot decompose the relations further

Key concepts

First Normal Form (1NF)

Database normalization is a process that optimizes the structure of database tables. First Normal Form (1NF) is the foundational step that ensures the basic structure of a database table. It emphasizes that all underlying data respects the principle of atomicity, which means each table cell should hold a singular value.
To satisfy 1NF, a table must not contain any repeating groups or arrays. For instance, if a book record has multiple authors stored in a single cell, it violates 1NF.
Ensuring 1NF guarantees that each piece of data is stored in its dedicated field, facilitating accurate querying and data manipulation.

Second Normal Form (2NF)

Second Normal Form (2NF) builds on 1NF by eliminating partial dependencies. Partial dependencies occur when a non-key attribute depends solely on a part of a composite primary key. For 2NF, it is essential that all non-key attributes are fully functionally dependent on the entire primary key.
In the exercise, assuming the primary key is Book_title, there are no partial dependencies present, meaning everything depends on the complete primary key. This is crucial in ensuring 2NF and leads to a more robust data structure that reduces redundancy.
Achieving 2NF involves evaluating the tables for any partial dependencies and restructuring them to maintain data atomicity and independence.

Third Normal Form (3NF)

Third Normal Form (3NF) furthers normalization by focusing on removing transitive dependencies, where a non-key attribute depends on another non-key attribute. It's about ensuring that every non-prime attribute is directly dependent on the primary key, not through another non-key attribute.
In the given exercise, there is a noted transitive dependency: Book_title depends on Book_type for Listprice, making it evident that the relation is not in 3NF initially. By decomposing the relation into two separate entities — one handling Book_type and Listprice, and the other managing the rest — the data integrity is maintained, and redundancy is reduced.
Achieving 3NF is critical for creating efficient database structures that prevent unnecessary multiplication of data.

Boyce-Codd Normal Form (BCNF)

After achieving 3NF, Boyce-Codd Normal Form (BCNF) is the next step. BCNF is an enhanced version of 3NF that ensures even stricter rules on the functional dependencies. A relation is in BCNF if, for every functional dependency (X → Y), X is a superkey.
The BCNF addresses anomalies that are not handled by 3NF, especially in complex database schemas. It guarantees that the database design is free from redundancy and dependency loops.
In the exercise, relations R1 and R2 both satisfy BCNF criteria, as every dependency's determinant in each relation forms a super key.
BCNF is pivotal for developers aiming to create databases that are scalable, efficient, and free from irregularities.