On Acyclic Database Decompositions.
STANFORD UNIV CA DEPT OF COMPUTER SCIENCE
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Given a universal relation scheme, presented as a set of attributes and a set of dependencies, it may be advantageous ot decompose it into a collection of schemes, each with its own sets of attributes and dependencies, which has some desired properties. A basic requirement for such a decomposition to be useful is that the corresponding decomposition map on universal relations be injective. A central problem in database theory is to find the reconstruction map, i.e., the inverse map of an injective decomposition map. We prove here that when the decomposition, viewed as a hypergraph, is acrylic and the given dependencies are full implicational dependencies, then the reconstruction map is the natural join. Based on this, we show that there is a polynomial time algorithm to test for injectiveness of decompositions.
- Theoretical Mathematics