Parallel Reasoning of Graph Functional Dependencies

This paper develops techniques for reasoning about graph functional dependencies (GFDs). We study the satisfiability problem, to decide whether a given set of GFDs has a model, and the implication problem, to decide whether a set of GFDs entails another GFD. While these fundamental problems are important in practice, they are coNP-complete and NP-complete, respectively. We establish a small model property for satisfiability, showing that if a set Sigma of GFDs is satisfiable, then it has a model of a size bounded by the size vertical bar Sigma vertical bar of Sigma; similarly we prove a small model property for implication. Based on the properties, we develop algorithms for checking the satisfiability and implication of GFDs. Moreover, we provide parallel algorithms that guarantee to reduce running time when more processors are used, despite the intractability of the problems. We experimentally verify the efficiency and scalability of the algorithms.