Decision Problems for Multivalued Dependencies in Relational Databases

Two decision problems related to multivalued dependencies in a relational database are considered. In this paper, an algorithm is presented for deciding whether or not a multivalued dependency can be derived from sets F of functional dependencies and M of multivalued dependencies on a set U of attributes, whose running time is proportional to min $(k^2 |U|,||F \cup M||^2 )$ where k and $|U|$ are the numbers of dependencies in $F \cup M$ and attributes in U, respectively, and $||F \cup M||$ is the size of description of F and M. A related algorithm is also considered which decides whether or not there exists a nontrivial multivalued dependency that is valid in a projection of the original relation.