 
Summary: Treewidth and functional dependencies in databases
Isolde Adler
HumboldtUniversit¨at zu Berlin, Institut f¨ur Informatik
adler@informatik.huberlin.de
5th December 2007
Abstract
Conjunctive query (CQ) evaluation on relational databases is NPcomplete in general.
Several restrictions, like bounded treewidth and bounded hypertreewidth, 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 nonrelational structures. We introduce the notions of closure
treewidth and hyperclosure treewidth for arbitrary structures, and we prove that HOM (and
hence CQ) restricted to bounded (hyper)closure treewidth becomes tractable. There are
classes of structures with bounded closure treewidth but unbounded treewidth. Similar
statements hold for hyperclosure treewidth and hypertreewidth, and for hyperclosure tree
width and closure treewidth.
It follows from a result by Gottlob, Mikl´os, and Schwentick that for fixed k 3, deciding
whether a given structure has hyperclosure treewidth at most k, is NPcomplete. We prove
an analogous statement for closure treewidth. Nevertheless, for given k we can approximate
kbounded closure treewidth in polynomial time.
