Conjunctive queries over trees

A framework for characterizing structures representing trees for which conjunctive queries can be evaluated efficiently and shows that for each conjunctive query, there is an equivalent acyclic positive query, but that in general this query is not of polynomial size.

Abstract

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structure are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated efficiently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subset maximal sets of axes for which query evaluation is in polynomial time. All polynomial-time results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.