Suppose that an application has four dimension tables, each of which contains 100 rows.

a. Determine the maximum number of rows in the fact table.
b. Suppose that a one-dimension table has an attribute that can take on 10 values.
Determine the size in bytes of a bit index on that attribute.
c. Determine the maximum number of tuples in a join index for a join between one of the dimension tables and the fact table.
d. Suppose that we use the CUBE operator on this fact table to perform aggregations on all four dimensions. Determine the number of rows in the resulting table.
e. Suppose that we use the ROLLUP operator on this fact table. Determine the number of rows in the resulting table.

a. The maximum number or rows in the fact table is 100 ? 100 ? 100 ? 100 = 108
b. The size of a bit index on that attribute is 100 ? 10/8 = 125 bytes.
c. The maximum size of a join index for a join between one of the dimension tables and the fact table is 108 rows. The reason for this is the following. Let Dimen-sionXYZ(DimensionId,...) be a dimension table and Fact(DimXYZ,...) be
a fact table. Then DimXYZ (which represents the values of dimension XYZ) must
be a foreign key referencing DimensionId, which is a key in DimensionXYZ.
Therefore, the number of tuples in the join (and therefore in the join index) is the
same as in the fact table.
d. The number of rows in the resulting table is
(100 ? 100 ? 100 ? 100) + (4 ? 100 ? 100 ? 100) + (4 ? 3 ? 100 ? 100/2)+
(4 ? 3 ? 2 ? 100/3 ? 2) + 1 =
108 + 4 ? 106 + 6 ? 104 + 4 ? 102 + 1
e. The number of rows in the resulting table is
(100 ? 100 ? 100 ? 100) + (100 ? 100 ? 100) + (100 ? 100) + 100 + 1 =
108 + 106 + 104 + 102 + 1