An efficient method for maintaining data cubes incrementally

The data cube operator computes group-bys for all possible combinations of a set of dimension attributes. Since computing a data cube typically incurs a considerable cost, the data cube is often precomputed and stored as materialized views in data warehouses. A materialized data cube needs to be updated when the source relations are changed. The incremental maintenance of a data cube is to compute and propagate only its changes, rather than recompute the entire data cube from scratch. For n dimension attributes, the data cube consists of 2ⁿ group-bys, each of which is called a cuboid. To incrementally maintain a data cube with 2ⁿ cuboids, the conventional methods compute 2ⁿ delta cuboids, each of which represents the change of a cuboid. In this paper, we propose an efficient incremental maintenance method that can maintain a data cube using only a subset of 2ⁿ delta cuboids. We formulate an optimization problem to find the optimal subset of 2ⁿ delta cuboids that minimizes the total maintenance cost, and propose a heuristic solution that allows us to maintain a data cube using only fenced((n; ⌈ n / 2 ⌉)) delta cuboids. As a result, the cost of maintaining a data cube is substantially reduced. Through various experiments, we show the performance advantages of the proposed method over the conventional methods. We also extend the proposed method to handle partially materialized cubes and dimension hierarchies.