Containment of data graph queries

The graph database model is currently one of the most popular paradigms for storing data, used in applications such as social networks, biological databases and the Semantic Web. Despite the popularity of this model, the development of graph database management systems is still in its infancy, and there are several fundamental issues regarding graph databases that are not fully understood. Indeed, while graph query languages that concentrate on topological properties are now well developed, not much is known about languages that can query both the topology of graphs and their underlying data. Our goal is to conduct a detailed study of static analysis problems for such languages. In this paper we consider the containment problem for several recently proposed classes of queries that manipulate both topology and data: regular queries with memory, regular queries with data tests, and graph XPath. Our results show that the problem is in general undecidable for all of these classes. However, by allowing only positive data comparisons we find natural fragments that enjoy much better static analysis properties: the containment problem is decidable, and its computational complexity ranges from PSPACE-complete to EXPSPACEcomplete. We also propose extensions of regular queries with an inverse operator, and study query evaluation and query containment for them