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.