Conjunctive queries over trees

Abstract

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures 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 subsetmaximal 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.

Conjunctive query containment over trees

“…, R k . We use the terminology on valuations of a query and query graphs from Gottlob et al [10]. Definition 1.…”

“…Recently, conjunctive queries have also been studied over tree structures [10]. It is somewhat surprising that they have not been studied earlier, as they arise very naturally in various settings, such as data extraction and integration, computational linguistics, and dominance constraints [10].…”

“…It is somewhat surprising that they have not been studied earlier, as they arise very naturally in various settings, such as data extraction and integration, computational linguistics, and dominance constraints [10]. Moreover, unary and binary conjunctive queries over trees form a very natural fragment of XPath 2.0 [2], and therefore also of XQuery [5].…”

“…Indeed, unary and binary conjunctive queries over trees are closely related to Core XPath without negation and union (see, e.g., [9]), but with path intersection, as introduced in XPath 2.0 (see, e.g., [11,16]). Gottlob et al already showed that unary conjunctive queries over trees can be translated to XPath 1.0 queries, albeit with an exponential blow-up [10], and the above-mentioned Core XPath queries with path intersection can be translated into conjunctive queries by identifying variables. Hence, our complexity upper bounds transfer to positive Core XPath expressions with path intersection, but without union.…”

L-wrappers: concepts, properties and construction

“…Combined complexity and expressivity results of conjunctive queries over trees, that also apply to information extraction, are reported in [15].…”