Path Constraints on Deterministic Graphs
Path constraints have been studied in [4, 10, 11] for semistructured data modeled as a rooted edge-labeled directed graph. They have proven useful in the optimization of path queries. However, in this graph model, the implication problems associated with many natural path constraints are undecidable . A variant of the graph model, called the deterministic data model, was recently proposed in . In this model, data is represented as a graph with deterministic edge relations, i.e, the edges emanating from any node in the graph have distinct labels. The deterministic graph model is more appropriate for representing, for example, ACeDB  databases and Web pages. This paper investigates path constraints for the deterministic data model. It demonstrates the application of path constraints to, among other things, query optimization. Four classes of path constraints are considered: the class of word constraints Pw proposed in , the constraint language Pc introduced in , an extension of Pc, denoted by Pc-, by including wild cards in path expressions, and a generalization of Pc-, denoted by Pc*, by representing paths as regular expressions. The implication problems for these constraint languages are studied in the context of the deterministic data model. It shows that the implication and finite implication problems for Pw are decidable in cubic-time and are finitely axiomatizable. Moreover, in contrast to the undecidability result of , these results also hold for Pc. In addition the implication problems are decidable for Pc-. However, the implication problems for Pc* are undecidable.