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.

Efficient Enumeration for Conjunctive Queries over X-underbar Structures

“…+ of the relations fc, ns and I t the identity relation on Dom(t). XPath axes are not X, and only some subsets of them are X, as shown in [13]. However as we will show, ACQS over XPath axes still enjoy good enumeration properties, mainly because of the following fact: In the context of XPath queries, it is important to consider the unary predicates lab a that test the labels of the nodes.…”

“…For instance, {child, next-sibling} are X for the order induced by a breadth-first left to right traversal of the tree. A complete list of subsets of tree relations (XPath axes) having the X property is established in [13].…”

“…In [13], a tractability frontier is established for conjunctive queries defined using XPath axes as predicates. This dichotomy relies on the X property (see Section 2 for a definition): if a structure S has the X property w.r.t.…”

“…5 Our first algorithm enumerates answers of an n-ary conjunctive query Q over an X structure S without preprocessing and with a delay in O(n·|S|·|Q|). The method relies on the computation of maximal arc-consistent pre-valuations proposed in [13]. We then turn to acyclic n-ary conjunctive queries (ACQS) Q over X structures S, and propose an algorithm with preprocessing O(|Q|·|S|) and delay in O(|Q|·|D|), where D is the domain of S. We first reason on a conceptually simpler notion of tree-shaped queries, namely tree patterns.…”

Monadic Datalog and Regular Tree Pattern Queries

“…Hence, translation from patterns to CQs involves quadratic blowup. As observed by Gottlob and Koch [15], each satisfiable graph pattern can be expressed as a union of TPQs, essentially reflecting possible ways of mapping the pattern to a tree. While the size of the TPQs can be bounded by the size of the pattern, their number is exponential.…”