Jarek Gryz

Skyline with presorting

The skyline, or Pareto, operator selects those tuples that are not dominated by any others. Extending relational systems with the skyline operator would offer a basis for handling preference queries. Good algorithms are needed for skyline, however, to make this efficient in a relational setting. We propose a skyline algorithm, SFS, based on presorting that is general, for use with any skyline query, efficient, and well behaved in a relational setting.

Algorithms and analyses for maximal vector computation

AbstractThe maximal vector problem is to identify the maximals over a collection of vectors. This arises in many contexts and, as such, has been well studied.The problem recently gained renewed attention with skyline queries for relational databases and with work to develop skyline algorithms that are external and relationally well behaved. While many algorithms have been proposed, how they perform has been unclear. We study the performance of, and design choices behind, these algorithms. We prove runtime bounds based on the number of vectors N and the dimensionality K. Early algorithms based on divide and conquer established seemingly good average and worst-case asymptotic runtimes. In fact, the problem can be solved in

Integrity constraints: semantics and applications

\mathcal{O}(KN)

Query folding with inclusion dependencies

average-case (holding K as fixed). We prove, however, that the performance is quite bad with respect to K. We demonstrate that the more recent skyline algorithms are better behaved, and can also achieve

Query rewriting using views in the presence of functional and inclusion dependencies

\mathcal{O}(KN)

Exploiting constraint-like data characterizations in query optimization

average-case. While K matters for these, in practice, its effect vanishes in the asymptotic. We introduce a new external algorithm, LESS, that is more efficient and better behaved. We evaluate LESS’s effectiveness and improvement over the field, and prove that its average-case running time is