Grouping and Aggregation (Relational Algebra)

relational-algebra

Definition

Grouping and Aggregation (Relational Algebra)

The grouping and aggregation operation, denoted by $\gamma$, is an operator that first partitions tuples of a relation $R$ into groups and then computes a single or multiple summary value for each group using an aggregate function.

This process involves two main steps:

1. Grouping: Tuples that have the same values for all attributes in a specified grouping list are placed into the same group.
2. Aggregation: An aggregate function (like SUM, COUNT, AVG, MIN, MAX) is applied to an attribute of the tuples within each group, producing a single value per group.

$${\gamma }_{L,F}(R)$$

where:

• $L$ is the list of attributes to group by
• $F$ is the aggregate function to be applied to each group. This also defines the new attribute for the aggregate value in the result schema (e.g., $F=\text{SUM}(\text{Price})\to \text{TotalValue}$)
• $R$ is the input relation

The resulting relation consists of the grouping attributes in $L$ and the new attribute(s) generated by the aggregate function(s) in $F$.