Rewriting with Acyclic Queries: Mind Your Head

The paper studies the rewriting problem, that is, the decision problem whether, for a given conjunctive query \(Q\) and a set \(\mathcal{V}\) of views, there is a conjunctive query \(Q'\) over \(\mathcal{V}\) that is equivalent to \(Q\), for cases where the query, the views, and/or the desired rewriting are acyclic or even more restricted. It shows that, if \(Q\) itself is acyclic, an acyclic rewriting exists if there is any rewriting. An analogous statement also holds for free-connex acyclic, hierarchical, and q-hierarchical queries. Regarding the complexity of the rewriting problem, the paper identifies a border between tractable and (presumably) intractable variants of the rewriting problem: for schemas of bounded arity, the acyclic rewriting problem is NP-hard, even if both \(Q\) and the views in \(\mathcal{V}\) are acyclic or hierarchical. However, it becomes tractable if the views are free-connex acyclic (i.e., in a nutshell, their body is (i) acyclic and (ii) remains acyclic if their head is added as an additional atom).