Answering Queries using Views over Probabilistic XML: Complexity and Tractability

TL;DR

This paper investigates the complexity of answering queries using views over probabilistic XML, identifying classes of XPath queries with efficient algorithms and analyzing the feasibility of probabilistic rewritings under different semantics.

Contribution

It introduces a comprehensive analysis of the complexity of probabilistic XML query rewriting, providing decision procedures and algorithms for cases with single and multiple views.

Findings

Efficient PTime algorithms exist for certain XPath queries with child and descendant navigation.

Probabilistic answer computation may be infeasible even when XML answers are retrievable from views.

The paper establishes conditions under which probabilistic rewriting is feasible and provides algorithms with soundness and completeness guarantees.

Abstract

We study the complexity of query answering using views in a probabilistic XML setting, identifying large classes of XPath queries -- with child and descendant navigation and predicates -- for which there are efficient (PTime) algorithms. We consider this problem under the two possible semantics for XML query results: with persistent node identifiers and in their absence. Accordingly, we consider rewritings that can exploit a single view, by means of compensation, and rewritings that can use multiple views, by means of intersection. Since in a probabilistic setting queries return answers with probabilities, the problem of rewriting goes beyond the classic one of retrieving XML answers from views. For both semantics of XML queries, we show that, even when XML answers can be retrieved from views, their probabilities may not be computable. For rewritings that use only compensation, we describe a PTime decision procedure, based on easily verifiable criteria that distinguish between the feasible cases -- when probabilistic XML results are computable -- and the unfeasible ones. For rewritings that can use multiple views, with compensation and intersection, we identify the most permissive conditions that make probabilistic rewriting feasible, and we describe an algorithm that is sound in general, and becomes complete under fairly permissive restrictions, running in PTime modulo worst-case exponential time equivalence tests. This is the best we can hope for since intersection makes query equivalence intractable already over deterministic data. Our algorithm runs in PTime whenever deterministic rewritings can be found in PTime.