Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals

Abstract

Data analysis applications typically aggregate data across manydimensions looking for anomalies or unusual patterns. The SQL aggregatefunctions and the GROUP BY operator produce zero-dimensional orone-dimensional aggregates. Applications need the N-dimensionalgeneralization of these operators. This paper defines that operator, calledthe data cube or simply cube. The cube operator generalizes the histogram,cross-tabulation, roll-up,drill-down, and sub-total constructs found in most report writers.The novelty is that cubes are relations. Consequently, the cubeoperator can be imbedded in more complex non-procedural dataanalysis programs. The cube operator treats each of the Naggregation attributes as a dimension of N-space. The aggregate ofa particular set of attribute values is a point in this space. Theset of points forms an N-dimensional cube. Super-aggregates arecomputed by aggregating the N-cube to lower dimensional spaces.This paper (1) explains the cube and roll-up operators, (2) showshow they fit in SQL, (3) explains how users can define new aggregatefunctions for cubes, and (4) discusses efficient techniques tocompute the cube. Many of these features are being added to the SQLStandard.