5.1 Assume that a 10-D base cuboid contains only three base cells: (1) (*a*_{1}, *d*_{2}, *d*_{3}, *d*_{4}, …, *d*_{9}, *d*_{10}), (2) (*d*_{1}, *b*_{2}, *d*_{3}, *d*_{4}, …, *d*_{9}, *d*_{10}), and (3) (*d*_{1}, *d*_{2}, *c*_{3}, *d*_{4}, …, *d*_{9}, *d*_{10}), where *a*_{1} ≠ *d*_{1}, *b*_{2} ≠ *d*_{2}, and *c*_{3} ≠ *d*_{3}. 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 ...

Start Free Trial

No credit card required