On the minimization of Xpath queries

XML queries are usually expressed by means of XPath expressions identifying portions of the selected documents. An XPath expression defines a way of navigating an XML tree and returns the set of nodes which are reachable from one or more starting nodes through the paths specified by the expression. The problem of efficiently answering XPath queries is very interesting and has recently received increasing attention by the research community. In particular, an increasing effort has been devoted to define effective optimization techniques for XPath queries. One of the main issues related to the optimization of XPath queries is their minimization. The minimization of XPath queries has been studied for limited fragments of XPath, containing only the descendent, the child and the branch operators. In this work, we address the problem of minimizing XPath queries for a more general fragment, containing also the wildcard operator. We characterize the complexity of the minimization of XPath queries, stating that it is NP-hard, and propose an algorithm for computing minimum XPath queries. Moreover, we identify an interesting tractable case and propose an ad hoc algorithm handling the minimization of this kind of queries in polynomial time.