Iceberg cubing is a valuable technique in data warehouses. The efficiency of iceberg cube computation comes from efficient aggregation and effective pruning for constraints. In advanced applications, iceberg constraints are often non-monotone and complex, for example, "Average cost in the range [δ_1, δ_2] and standard deviation of cost less than β". The current cubing algorithms either are efficient in aggregation but weak in pruning for such constraints, or can prune for non-monotone constraints but are inefficient in aggregation. The best algorithm of the former, Star-cubing, computes aggregations of cuboids simultaneously but its pruning is specific to only monotone constraints such as "COUNT(*) ≥ δ". In the latter case, the Divide and Approximate pruning technique can prune for non-monotone constraints but is limited to bottom-up single-group aggregation. We propose a solution that exhibits both efficiency in aggregation and generality and effectiveness in pruning for complex constraints. Our bounding techniques are as general as the Divide and Approximate pruning techniques for complex constraints and yet our multiway aggregation is as efficient as Star-cubing.
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