Relational Algebra Operations

• Relational algebra is a procedural query language.

Fundamental Operations

• Selection: selects tuples from a relation that satisfy a given condition.
• Projection: retains specified attributes from a relation.
• Union: combines tuples from two compatible relations.
• Set Difference: identifies tuples present in one relation but not the other.
• Cartesian Product: combines each tuple of one relation with each tuple of another.
• Renaming: renames a relation or its attributes.

Additional Operations

• These can be defined using fundamental operations and simplify common queries.
• Set Intersection: identifies tuples common to two relations.
• Join: combines tuples from two relations based on a condition.
• Division: identifies tuples in one relation that correspond to all tuples in another.

Example Relations

• Consider these relations:
  • Employees (employee_id, name, address, salary)
  • Departments (department_id, department_name, location)
  • Assignments (employee_id, department_id, time_percentage)

Examples Queries

• Find employees who earn more than €50,000:
  • σ salary > 50000 (Employees)
• Find the names and addresses of all employees:
  • π name, address (Employees)
• Find the employees who work in the "IT" department:
  • π name (σ department_name = "IT" (Departments ⋈ Assignments ⋈ Employees))

Relational Algebra Operators

• Selection: σ
• Projection: π
• Union: ∪
• Set Difference: -
• Cartesian Product: ×
• Renaming: ρ
• Natural Join: ⋈
• Division: ÷
• Intersection: ∩

Key Takeaways

• Relational algebra is a formal language with a well-defined syntax and semantics.
• It forms the basis for many database query languages, such as SQL.
• Understanding relational algebra is essential for optimizing database queries.

Conclusion

• Relational algebra provides a powerful set of operations for manipulating data in relational databases.
• Its understanding is crucial for query design and optimization.