Containment and equivalence for an XPath fragment

XPath is a simple 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 paper 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 which 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 EXPTIME algorithm for containment, and study parameterized PTIME special cases. While we identify two parameterized classes of queries for which containment can be decided efficiently, we also show that even with some bounded parameters, containment is coNP-complete. In response to these negative results, we describe a sound algorithm which is efficient for all queries, but may return false negatives in some cases.