Containment and equivalence for a fragment of XPath

XPath is a language for navigating an XML document and selecting a set of element nodes. XPath expressions are used to query XML data, describe key constraints, express transformations, and reference elements in remote documents. This article studies the containment and equivalence problems for a fragment of the XPath query language, with applications in all these contexts. In particular, we study a class of XPath queries that contain branching, label wildcards and can express descendant relationships between nodes. Prior work has shown that languages that combine any two of these three features have efficient containment algorithms. However, we show that for the combination of features, containment is coNP-complete. We provide a sound and complete algorithm for containment that runs in exponential time, and study parameterized PTIME special cases. While we identify one parameterized class of queries for which containment can be decided efficiently, we also show that even with some bounded parameters, containment remains coNP-complete. In response to these negative results, we describe a sound algorithm that is efficient for all queries, but may return false negatives in some cases.