OLAP Operations

OLAP tools let users navigate a multidimensional data cube through five core operations:

1. Roll-up (Drill-up)

Aggregates data by climbing up a concept hierarchy or reducing dimensions.

Day → Month → Quarter → Year        (climbing the Time hierarchy)

Example: Sales by City → Sales by State → Sales by Country.

2. Drill-down

The reverse of roll-up — moves down the hierarchy to reveal finer detail.

Year → Quarter → Month → Day

Example: Yearly sales → Quarterly sales → Monthly sales.

3. Slice

Selects a single value on one dimension, producing a lower-dimensional sub-cube.

Cube(Time, Product, Region) --Time="2024"--> Table(Product, Region)

4. Dice

Selects a sub-cube by specifying ranges/values on two or more dimensions.

Dice: Time∈{2023,2024}, Region="West" → smaller cube

5. Pivot (Rotate)

Rotates the data axes to provide an alternate presentation — e.g., swapping rows and columns in a cross-tab.

Before:                 After pivot:
        Q1  Q2  Q3            Prod A  Prod B
Prod A  10  20  15    ──▶  Q1   10      12
Prod B  12  18  22          Q2   20      18
                             Q3   15      22

Summary Table

Operation	Effect	Dimensionality change
Roll-up	Aggregate, coarsen granularity	Decreases (or stays, fewer dims)
Drill-down	Disaggregate, finer granularity	Increases
Slice	Fix one dimension's value	Decreases by 1
Dice	Restrict 2+ dimensions	Same dims, smaller sub-cube
Pivot	Re-orient axes for viewing	Unchanged

These operations give analysts an interactive way to explore a cube from summary to detail and back, without re-running queries against the raw source data.