Skycube Materialization Using the Topmost Skyline or Functional Dependencies
Résumé
Given a table T(Id, D1, …, Dd), the skycube of T is the set of skylines with respect to to all nonempty subsets (subspaces) of the set of all dimensions {D1, …, Dd}. To optimize the evaluation of any skyline query, the solutions proposed so far in the literature either (i) precompute all of the skylines or (ii) use compression techniques so that the derivation of any skyline can be done with little effort. Even though solutions (i) are appealing because skyline queries have optimal execution time, they suffer from time and space scalability because the number of skylines to be materialized is exponential with respect to d. On the other hand, solutions (ii) are attractive in terms of memory consumption, but as we show, they also have a high time complexity. In this article, we make contributions to both kinds of solutions. We first observe that skyline patterns are monotonic. This property leads to a simple yet efficient solution for full and partial skycube materialization when the skyline with respect to all dimensions, the topmost skyline, is small. On the other hand, when the topmost skyline is large relative to the size of the input table, it turns out that functional dependencies, a fundamental concept in databases, uncover a monotonic property between skylines. Equipped with this information, we show that closed attributes sets are fundamental for partial and full skycube materialization. Extensive experiments with real and synthetic datasets show that our solutions generally outperform state-of-the-art algorithms.