Tree-width and functional dependencies in databases

Abstract

Conjunctive query (CQ) evaluation on relational databases is NP-complete in general. Several restrictions, like bounded and bounded hypertree-width, allow polynomial time evaluations.We extend the framework in the presence of functional dependencies. Our exteAnded CQ evaluation problem has a concise equivalent formulation in terms of the homomorphism problem (HOM) for non-relational structures. We introduce the notions of tree-width and tree-width for arbitrary structures, and we prove that HOM (and hence CQ) restricted to bounded (hyper)closure becomes tractable. There are classes of structures with bounded closure but unbounded tree-width. Similar statements hold for hyperclosure and hypertree-width, and for hyperclosure and closure tree-width.It follows from a result by Gottlob, Miklos, and Schwentick that for fixed k ≥ 2, deciding whether a given structure has hyperclosure at most k, is NP-complete. We prove an analogous statement for closure tree-width. Nevertheless, for given k we can approximate k-bounded closure in polynomial time.