On acyclic database decompositions

Catriel Beeri, Moshe Y. Vardi
1984 Information and Control  
Given a universal relation scheme, presented as a set of attributes and a set of dependencies, it may be advantageous to decompose it into a collection of schemes, each with its own sets of attributes and dependencies, that 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
more » ... e decomposition map. It is proved here that when the decomposition, viewed as a hypergraph, is acyclic and the given dependencies are full implicational dependencies, then the reconstruction map is the natural join. Based on this, it is shown that there is a polynomial time algorithm to test for injectiveness of decompositions.
doi:10.1016/s0019-9958(84)80051-0 fatcat:baqmpsa4oza6dba765npcetqcq