Fact Table Tuple Count with GROUP BY CUBE

This solution calculates the number of tuples generated by a $GROUP BY CUBE$ query on a given fact table structure.

Understanding GROUP BY CUBE

The $GROUP BY CUBE$ clause generates all possible grouping combinations (grouping sets) for the specified dimensions, including the grand total. For dimensions D1 and D2, the grouping sets are:

• $(D1, D2)$: Aggregation for every combination of D1 and D2 values.
• $(D1)$: Aggregation for each D1 value (subtotal across D2).
• $(D2)$: Aggregation for each D2 value (subtotal across D1).
• $()$: The grand total (aggregation across all dimensions).

Fact Table Dimensions

The problem specifies a fact table with dimensions:

• Dimension $D1$ has 3 distinct values.
• Dimension $D2$ has 2 distinct values.

It's stated that all combinations of these values exist in the fact table.

Calculating Tuple Count

We can determine the total number of tuples by summing the counts from each grouping set:

• Tuples for $(D1, D2)$: Number of D1 values $\times$ Number of D2 values = $3 \times 2 = 6$.
• Tuples for $(D1)$: Number of D1 values = $3$.
• Tuples for $(D2)$: Number of D2 values = $2$.
• Tuple for $()$ (Grand Total): $1$.

Total tuples = $6 + 3 + 2 + 1 = 12$.

Alternatively, a direct formula for the size of a $CUBE$ operation on dimensions with $n_1, n_2, ..., n_k$ distinct values is:

$ (n_1 + 1) \times (n_2 + 1) \times \dots \times (n_k + 1) $

For this case (D1 and D2):

$ (3 + 1) \times (2 + 1) $

$ 4 \times 3 $

$ 12 $

Final Result

The query using $GROUP BY CUBE (D1, D2)$ will produce 12 tuples.