Between Tree Patterns and Conjunctive Queries: Is There Tractability beyond Acyclicity?

In static analysis of queries over trees in the presence of schemas, there is an exponential complexity gap between conjunctive queries (CQs, positive existential first-order formulae without disjunction) and tree patterns (tree-like acyclic CQs). Motivated by applications in XML data management, we consider various restrictions of CQs that bring their complexity down to that of tree patterns. Most importantly, we show that vertical tree patterns can be costlessly extended with full horizontal CQs over children. We also consider restricted classes of schemas and show that under disjunction-free schemas the complexity of static analysis sometimes drops dramatically.