  This paper investigates the impact of query topology on the difficulty of
answering conjunctive queries in the presence of OWL 2 QL ontologies. Our first
contribution is to clarify the worst-case size of positive existential (PE),
non-recursive Datalog (NDL), and first-order (FO) rewritings for various
classes of tree-like conjunctive queries, ranging from linear queries to
bounded treewidth queries. Perhaps our most surprising result is a
superpolynomial lower bound on the size of PE-rewritings that holds already for
linear queries and ontologies of depth 2. More positively, we show that
polynomial-size NDL-rewritings always exist for tree-shaped queries with a
bounded number of leaves (and arbitrary ontologies), and for bounded treewidth
queries paired with bounded depth ontologies. For FO-rewritings, we equate the
existence of polysize rewritings with well-known problems in Boolean circuit
complexity. As our second contribution, we analyze the computational complexity
of query answering and establish tractability results (either NL- or
LOGCFL-completeness) for a range of query-ontology pairs. Combining our new
results with those from the literature yields a complete picture of the
succinctness and complexity landscapes for the considered classes of queries
and ontologies.
