TY - JOUR
T1 - On acyclic database decompositions
AU - Beeri, Catriel
AU - Vardi, Moshe Y.
PY - 1984/5
Y1 - 1984/5
N2 - 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 injective 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.
AB - 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 injective 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.
UR - http://www.scopus.com/inward/record.url?scp=0021425641&partnerID=8YFLogxK
U2 - 10.1016/S0019-9958(84)80051-0
DO - 10.1016/S0019-9958(84)80051-0
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AN - SCOPUS:0021425641
SN - 0019-9958
VL - 61
SP - 75
EP - 84
JO - Information and control
JF - Information and control
IS - 2
ER -