Discovery-driven cube exploration is a desirable way to mark interesting points among a large number of cells in a data cube. Individual users may have different views on whether a point should be considered interesting enough to be marked. Suppose one would like to mark those objects of which the absolute value of z score is over 2 in every row and column in a d-dimensional plane.

(a) Derive an efficient computation method to identify such points during the data cube computation.

(b) Suppose a partially materialized cube has (d - 1)-dimensional and (d + 1)- dimensional cuboids materialized but not the d-dimensional one. Derive an efficient method to mark those (d - 1)-dimensional cells with d-dimensional children that contain such marked points.