On the existence of acyclic views in a database scheme (Q1060030)

The importance of acyclic database schemes in relational database theory has been pointed out in various contributions in the literature. Unfortunately, the realm of interest which is captured by the database scheme is often intrinsically cyclic; therefore, we are faced with the problem of finding acyclic views on such a scheme. In this paper we consider three kinds of acyclicity, called \(\alpha\)-, \(\gamma\)- and Berge-acyclicity by Fagin (1983), and we approach the problem of the existence of acyclic views in a database scheme. We show that the problem of deciding whether there exists a Berge-, \(\gamma\)-, or \(\alpha\)-acyclic view in a general database scheme is NP-complete and that the problem of deciding whether there exists a Berge- or \(\gamma\)-acyclic view on an \(\alpha\)-acyclic scheme is also computationally intractable. On the other hand, if the given database scheme is \(\gamma\)-acyclic, the problem of deciding the existence of a Berge-acyclic view may be solved by means of efficient algorithms which may also be used to find an acyclic view which involves the minimum number of relations.