The sampling cube was proposed for multidimensional analysis of sampling data (e.g., survey data). In many real applications, sampling data can be of high dimensionality (e.g., it is not unusual to have more than 50 dimensions in a survey data set).

a. How can we construct an efficient and scalable high-dimensional sampling cube in large sampling data sets?

b. Design an efficient incremental update algorithm for such a high-dimensional sampling cube.

c. Discuss how to support quality drill-down given that some low-level cells may be empty or contain too few data for reliable analysis.