Semantically Acyclic Conjunctive Queries under Functional Dependencies

The evaluation problem for Conjunctive Queries (CQ) is known to be NP-complete in combined complexity and W[1]-hard in parameterized complexity. However, acyclic CQs and CQs of bounded tree-width can be evaluated in polynomial time in combined complexity and they are fixed-parameter tractable.We study the problem of whether a CQ can be rewritten into an equivalent CQ of bounded tree-width, in the presence of unary functional dependencies, assuming bounded arity signatures. We show that this problem is decidable in doubly exponential time, or in exponential time for a subclass of CQ’s. When it exists, the algorithm also yields a witness query.