When working with the relational model, there are two groups of operations that can be used. One of these is known as relational algebra, which serves as the basis for SQL, the widely-used language for working with relational databases. The other group is relational calculus, which takes a declarative approach to interacting with databases. In this blog, we will focus on relational algebra and its primary and join operations.

Primary Operations in Relational Algebra

Primary operations are the foundational operations in relational algebra. These include:

  1. Union: This operation combines data from two tables, generating a sum of the tuples. It is only possible if the two tables have the same columns and attribute types (domain).

  2. Difference: With this operation, we can obtain data that is present in the first table but not in the second table. It generates a difference of the tuples and requires the two tables to have the same columns and attribute types.

  3. Cartesian Product: The Cartesian product combines data from two tables, allowing for the generation of one single table that combines the data. It is based on an attribute value.

  4. Select: This operation extracts specific tuples (rows) from a table based on certain criteria.

  5. Project: Project creates a new table containing only one or more attributes (columns) of an existing table.

  6. Rename: This operation is used to rename an attribute, preventing conflicts when multiple tables have the same name for different data.

Join Operations in Relational Algebra

Join operations in relational algebra allow for the correlation of data contained in different relations (tables). These operations build on top of primary operations and provide a powerful way to combine data. The two main join operations are:

  1. Natural Join: The natural join correlates two relations (tables) and creates a new table based on the same values of an attribute. It requires two relations to have the same attribute name (column). If values in the attributes in one relation are unmatched in the attributes in the other relation, those rows are not included in the result.

  2. Theta Join: Theta join allows for a join based on any criteria to compare two columns in two different relations, rather than just equality like the natural join. It performs a cartesian product of the two tables and filters the results based on the desired selection.

Equi-join is a type of theta join where the selection is based on equality between attribute values in the two different tables.

These join operations provide powerful ways to combine and correlate data, and we will discuss them in more detail when we introduce SQL.

In conclusion, relational algebra is a fundamental part of working with relational databases. By understanding the primary and join operations, you can effectively manipulate and combine data in these databases. With SQL being the de-facto language for working with relational databases, knowing relational algebra becomes even more crucial.

Tags: relational algebra, primary operations, join operations, union, difference, cartesian product, select, project, rename, natural join, theta join