XPath query containment

Consider an XML publish-subscribe scenario with hundreds of subscribers and tens of thousands of XML documents to be delivered per day. Subscribers specify the documents in which they are interested in by means of XPath [8] expressions. If an expression matches a (part of a) document it is delivered to the subscriber. Naturally, it is desired that the decision to which subscriber a document must be sent should be taken quickly. Although the test whether a single XPath expression matches can be done in polynomial time, it is not efficient to test every such expression for every document. Fortunately, there is a partial order on expressions, i.e., for some expressions p, q it might hold that whenever a document matches p it also matches q (denoted p ⊆0 q). If we already know that a document matches p, we do not need to test q anymore, as it matches automatically. Correspondingly, if we know that q does not match then p will not match either. Hence, the inclusion structure of the XPath expressions should be computed in advance to decrease online computation time. This leads to the algorithmic problem of XPath Query Containment, i.e., checking whether p ⊆0 q (for a different, indexbased approach see, e.g., [6]). The main idea of this article is to describe some of the main algorithmic techniques that have been proposed for XPath Query Containment. These techniques are described in Section 5. Before that, in Sections 2 and 3 the basic definitions on XPath and the