218 Chapter 5 Data Cube Technology and E, where AB has the instantiation (a 2 , b 1 ). The fetch of the TID lists for these parti- tions returns (a 2 , b 1 ) : {4, 5}, (c 1 ) : {1, 2, 3, 4, 5} and {(e 1 : {1, 2}), (e 2 : {3, 4}), (e 3 : {5})}, respectively. The intersection of these corresponding TID lists contains a cuboid with two tuples: {(c 1 , e 2 ) : {4}, 5 (c 1 , e 3 ) : {5}}. This base cuboid can be used to compute the 2-D data cube, which is trivial. For large data sets, a fragment size of 2 or 3 typically results in reasonable storage requirements for the shell fragments and for fast query response time. Querying with shell fragments is substantially faster than answering queries using precomputed data cubes that are stored on disk. In comparison to full cube computation, Frag-Shells is recommended if there are less than four inquired dimensions. Otherwise, more efficient algorithms, such as Star-Cubing, can be used for fast online cube computation. Frag- Shells can be easily extended to allow incremental updates, the details of which are left as an exercise. 5.3 Processing Advanced Kinds of Queries by Exploring Cube Technology Data cubes are not confined to the simple multidimensional structure illustrated in the