Ronald Fagin
R. Guha
ABSTRACT
We introduce the Multi-Structural Database, a new data framework to support efficient analysis of large, complex data sets. An instance of the model consists of a set of data objects, together with a schema that specifies segmentations of the set of data objects according to multiple distinct criteria (e.g., into a taxonomy based on a hierarchical attribute). Within this model, we develop a rich set of analytical operations and design highly efficient algorithms for these operations. Our operations are formulated as optimization problems, and allow the user to analyze the underlying data in terms of the allowed segmentations.
Our algorithms and results extend those of Fagin et al. [8] who studied composition of mappings given by several kinds of constraints. In particular, they proved that full source-to-target tuple-generating dependencies (tgds) are closed under composition, but embedded source-to-target tgds are not. They introduced a class of second-order constraints, <i>SO tgds</i>, that is closed under composition and has desirable properties for data exchange.
We study constraints that need not be source-to-target and we concentrate on obtaining (first-order) embedded dependencies. As part of this study, we also consider full dependencies and second-order constraints that arise from Skolemizing embedded dependencies. For each of the three classes of mappings that we study, we provide (a) an algorithm that attempts to compute the composition and (b) sufficient conditions on the input mappings that guarantee that the algorithm will succeed.
In addition, we give several negative results. In particular, we show that full dependencies are not closed under composition, and that second-order dependencies that are not limited to be source-to-target are not closed under restricted composition. Furthermore, we show that determining whether the composition can be given by these kinds of dependencies is undecidable.
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