Minimal coverage of generalized typed inclusion dependencies in databases

The paper discusses the theory and algorithms necessary to construct a minimal covering of generalized typed inclusion dependencies. Traditionally, the construction of minimal covering is used for all types of dependencies in order to obtain a non-redundant and consistent database design. Generalized inclusion dependencies correspond to referential integrity constraints, when several main and several external relations are involved in one constraint, which corresponds to an ultragraph edge. In previous work, based on a study of the properties of dependencies, a system of axioms was presented with proof of consistency and completeness. In this work, the closures were studied for generalized typed inclusion dependencies. An algorithm for constructing closures has been developed and its correctness has been proven. The results obtained are further used to develop an algorithm for constructing a minimal covering. At the end of the article, examples are presented that demonstrate the operation of the algorithms.