C-cubing: Efficient computation of closed cubes by aggregation-based checking

It is well recognized that data cubing often produces huge outputs. Two popular efforts devoted to this problem are (1) iceberg cube, where only significant cells are kept, and (2) closed cube, where a group of cells which preserve roll-up/drill-down semantics are losslessly compressed to one cell. Due to its usability and importance, efficient computation of closed cubes still warrants a thorough study. In this paper, we propose a new measure, called closedness, for efficient closed data cubing. We show that closedness is an algebraic measure and can be computed efficiently and incrementally. Based on closedness measure, we develop an an aggregation-based approach, called C-Cubing (i.e., Closed-Cubing), and integrate it into two successful iceberg cubing algorithms: MM-Cubing and Star-Cubing. Our performance study shows that C-Cubing runs almost one order of magnitude faster than the previous approaches. We further study how the performance of the alternative algorithms of C-Cubing varies w.r.t the properties of the data sets.