Chasing Tree Patterns under Recursive DTDs

Abstract

Finding a homomorphism between tree patterns is an important technique for testing tree pattern containment, and it is the main technique behind algorithms for rewriting tree pattern queries using views. Recent work has shown that for tree patterns P and Q that involve parent-child (/) edges, ancestor-descendant (//) edges, and branching ([]) only, under a non-disjunctive, non-recursive dtd G, testing whether P is contained in Q can be done by chasing P into P′ using five types of constraints derivable from G, and then testing whether P′ is contained in Q without G, which in turn can be done by finding a homomorphism from Q to P′. We extend this work to non-disjunctive, recursive dtds. We identify three new types of constraints that may be implied by a non-disjunctive recursive dtd, and show that together with the previous five types of constraints, they are necessary, and sufficient in some important cases, to consider for testing containment of tree patterns involving /, //, and [] under G. We present two sets of chase rules to chase a tree pattern repeatedly, and compare the advantages of these chase rules.