Minimal Covering of Generalized Typed Inclusion Dependencies in Databases

The theory and algorithms required to construct the minimal covering of generalized typed inclusion dependencies are discussed. Traditionally, the construction of the minimal covering is used for all types of dependencies in order to obtain a nonredundant and consistent database design. Generalized inclusion dependencies correspond to referential integrity constraints, when several main relations and several external relations are involved in one constraint, which corresponds to an ultragraph edge. A system of axioms with proof of consistency and completeness based on the study of dependency properties is presented in the previous study. In this study, closures for generalized typed inclusion dependencies are studied. An algorithm for constructing closures is developed. The correctness of the algorithm is proved. The results are further used to develop an algorithm for constructing the minimum covering. Examples that demonstrate the operation of the algorithms are presented at the end of the article.