In multidimensional data analysis, it is interesting to extract pairs of similar cell characteristics associated with substantial changes in measure in a data cube, where cells are considered similar if they are related by roll-up (i.e., ancestors), drill-down (i.e., descendants), or 1-D mutation (i.e., siblings) operations. Such an analysis is called cube gradient analysis.

Suppose the measure of the cube is average. A user poses a set of probe cells and would like to find their corresponding sets of gradient cells, each of which satisfies a certain gradient threshold. For example, find the set of corresponding gradient cells that have an average sale price greater than \(20 \%\) of that of the given probe cells. Develop an algorithm than mines the set of constrained gradient cells efficiently in a large data cube.