Tree-width and functional dependencies in databases

• Authors: Isolde Adler
• Venue: Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
• Year: 2008

Conjunctive query (CQ) evaluation on relational databases is NP-complete in general. Several restrictions, like bounded tree-width 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 "closure tree-width" and "hyperclosure tree-width" for arbitrary structures, and we prove that HOM (and hence CQ) restricted to bounded (hyper)closure tree-width becomes tractable. There are classes of structures with bounded closure tree-width but unbounded tree-width. Similar statements hold for hyperclosure tree-width and hypertree-width, and for hyperclosure tree-width and closure tree-width. It follows from a result by Gottlob, Miklós, and Schwentick that for fixed k ≥ 2, deciding whether a given structure has hyperclosure tree-width 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 tree-width in polynomial time.