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## 5.6 Exercises

5.1 Assume that a 10-D base cuboid contains only three base cells: (1) (a1, d2, d3, d4, …, d9, d10), (2) (d1, b2, d3, d4, …, d9, d10), and (3) (d1, d2, c3, d4, …, d9, d10), where a1d1, b2d2, and c3d3. The measure of the cube is count().

(a) How many nonempty cuboids will a full data cube contain?

(b) How many nonempty aggregate (i.e., nonbase) cells will a full cube contain?

(c) How many nonempty aggregate cells will an iceberg cube contain if the condition of the iceberg cube is “count ≥ 2”?

(d) A cell, c, is a closed cell if there exists no cell, d, such that d is a specialization of cell c (i.e., d is obtained by replacing a ∗ in c by a non-∗ value) and d has the same measure value as c. A closed cube is a data cube ...

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