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Necessary Conditions and Algorithm for Decompositing Relational Schema under Null Value Circumstances into BCNF Without Loss Joins

YE Yang ming (Dept. of Compu. Sci. Xiamen Univ.,Xiamen 361005,China)  
The necessary condition of decompositons for relational scheme under null value circumstances into BCNF without loss joins, which was presented in Ref.[1],is proved to be wrong. Two new necessary conditions are presented. They are given separately from the minimal set F′ and the Closure F + of the functional dependencies F of the relational scheme. Two algorithms for decomposing relational scheme under null value circumstances into BCNF without loss joins are given. These algorithms use binary tree for search. The scheme which is not in BCNF is decomposed into two subschemes without loss joins, and one can get one predecessor node and two successor nodes. If possible, one can construct the same decomposition again and again; Otherwise, one must back into its predeccessor node and try new decomposition. In the end, one can get the result that fits into the demand(all leaf nodes are (N)BCNF), or else, the information which showed that impossible to be decomposed is output. One algorithm is simple, yet it cannot get all possible decompositions which satisfy the demand. The other algorithm is more complex, but it can get all possible decompositions satisfying the demand.
【Fund】: 国家自然科学基金!(69383004)
【CateGory Index】: TP301.6
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