Complex Aggregation at Multiple Granularities

Datacube queries compute simple aggregates at multiple gran-ularities. In this paper we examine the more general and useful problem of computing a complex subquery involving multiple dependent aggregates at multiple granularities. We call such queries \multi-feature cubes." An example is \Broken down by all combinations of month and customer, nd the fraction of the total sales in 1996 of a particular item due to suppliers supplying within 10% of the minimum price (within the group), showing all subtotals across each dimension." We classify multi-feature cubes based on the extent to which ne granularity results can be used to compute coarse granularity results; this classiication includes distribu-tive, algebraic and holistic multi-feature cubes. We provide syntactic suucient conditions to determine when a multi-feature cube is either dis-tributive or algebraic. This distinction is important because, as we show, existing datacube evaluation algorithms can be used to compute multi-feature cubes that are distributive or algebraic, without any increase in I/O complexity. We evaluate the CPU performance of computing multi-feature cubes using the datacube evaluation algorithm of Ross and Srivastava. Using a variety of synthetic, benchmark and real-world data sets, we demonstrate that the CPU cost of evaluating distributive multi-feature cubes is comparable to that of evaluating simple datacubes. We also show that a variety of holistic multi-feature cubes can be evaluated with a manageable overhead compared to the distributive case.