The Theory of Joins in Relational Databases

Answering queries in a relational database often requires that the natural join of two or more relations be computed. However, the result of a join may not be what one expects. In this paper we give efficient algorithms to determine whether the join of several relations has the intuitively expected value (is lossless) and to determine whether a set of relations has a subset with a lossy join. These algorithms assume that all data dependencies are functional. We then discuss the extension of our techniques to the case where data dependencies are multivalued.