On the equivalence of an Egd to a set of Fd's

• Authors: Marc H. Graham;Ke Wang
• Venue: Journal of the ACM (JACM)
• Year: 1990

The question “Is a given join dependency equivalent to some set of multivalued dependencies?” led to the development of acyclicity theory [1]. The central question of this paper is: “Is a given equality-generating dependency equivalent to a set of functional dependencies?” An algorithm is presented that answers that question in polynomial time without using the chase process and, in the case of a “yes” answer, can be used to find (a cover of) the set of functional dependencies involved. This question is also related to the similar question about join dependencies and multivalued dependencies by proving a result about the hypergraph representation of an egd. It is interesting to note that a minimal representation of an egd must be &bgr;-acyclic for the egd to be equivalent to a set of fd's, in contrast to the jd/mvd case, in which only &agr;-acyclicity is needed. The &bgr;-acyclicity of an egd not necessarily minimal is always sufficient for the egd to be equivalent to a set of fd's as shown. Finally, the algorithm is extended for a single egd to answer the question whether a set of egd's with the same right-hand-side column is equivalent to a set of fd's.