Summary: Tree-width and functional dependencies in databases
Humboldt-Universit¨at zu Berlin, Institut f¨ur Informatik
5th December 2007
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
extended CQ evaluation problem has a concise equivalent formulation in terms of the homo-
morphism 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, Mikl´os, and Schwentick that for fixed k 3, 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.