A Revisiting “Forward node-selecting queries over trees”

XML is a World Wide Web Consortium (W3C) standard for tree-structured data. XPath [Clark and DeRose 1999] is an important language widely employed in XML query, transformation, and update languages. XPath is a language of path expressions that can be viewed as defining sets of nodes of a tree, by following axis steps and applying node tests or path-existence filters to navigate from the root of the tree. For example, the XPath expression /descendant::A[child::B] selects all nodes in the tree below the root whose label is A and that have a child labeled B; here, descendant and child are axis steps, and the brackets indicate a filter that tests for the existence of a path matching the expression inside. A significant complication in XPath is the presence of both forward and reverse axis steps. If implemented naively, by for example repeatedly traversing the tree in forward or backward directions, queries that mix forward and reverse edges can be very expensive to evaluate. For example, an XPath query