Often, the aggregate count value of many cells in a large data cuboid is zero, resulting in a huge, yet sparse, multidimensional matrix.
(a) Design an implementation method that can elegantly overcome this sparse matrix problem. Note that you need to explain your data structures in detail and discuss the space needed, as well as how to retrieve data from your structures.
(b) Modify your design in (a) to handle incremental data updates. Give the reasoning behind your new design.