Fig. 1. Two views on the line item cube.

Fig. 2. Hierarchies in the LI and PS schemes (in gray the dimensions).

Fig. 3. Roll-up relationships between grouping sets on the LI scheme.

Fig. 4. Sets of the x_ijk (left) and y_jk (right) for fragmentation in Section 3.1.

Fig. 5. Fragmented and unfragmented workload costs for Q₁ (top), Q₂ (middle), and Q₃ (bottom) varying the space constraints.

Fig. 6. Number of fragments and views materialized for different disk space constraints (data are averaged on the three workloads).

Fig. 7. Percentage of replicated keys and percentage of measures (data are averaged on the three workloads).

Table 1. Execution costs

A dash denotes that a query cannot be executed on a view/fragment, the costs in parentheses denote that not all the measures required by the query are found on the fragment.

Table 2. Comparison of materialization solutions

Table 3. Notation employed for index sets in the IP formulation of VFP

Table 4. Shift from optimality induced by the heuristic reduction of the set of candidate views on the materialization solution for Q₁ with 1.4 GB available

Table 5. Cost of a workload when executed on the materialization solution optimized for itself and for Q₁ (with space constraint 1 GB)

Table 6. Computational test summary results