On the minimization of XPath queries

Abstract

XPath expressions define navigational queries on XML data and are issued on XML documents to select sets of element nodes. Due to the wide use of XPath, which is embedded into several languages for querying and manipulating XML data, the problem of efficiently answering XPath queries has received increasing attention from the research community. As the efficiency of computing the answer of an XPath query depends on its size, replacing XPath expressions with equivalent ones having the smallest size is a crucial issue in this direction. This article investigates the minimization problem for a wide fragment of XPath (namely X P [/ * ] ), where the use of the most common operators (child, descendant, wildcard and branching) is allowed with some syntactic restrictions. The examined fragment consists of expressions which have not been specifically studied in the relational setting before: neither are they mere conjunctive queries (as the combination of "// " and " * " enables an implicit form of disjunction to be expressed) nor do they coincide with disjunctive ones (as the latter are more expressive). Three main contributions are provided. The "global minimality" property is shown to hold: the minimization of a given XPath expression can be accomplished by removing pieces of the expression, without having to re-formulate it (as for "general" disjunctive queries). Then, the complexity of the minimization problem is characterized, showing that it is the same as the containment problem. Finally, specific forms of XPath expressions are identified, which can be minimized in polynomial time.

Revisiting redundancy and minimization in an XPath fragment

“…The flaw in [4] led them to the conclusion that a pattern P is non-redundant if for all nodes n of P , the sub-pattern rooted at n has no redundant branch that emanates from n. But we give a counterexample to this claim. Hence, the algorithm of [4] (which tests containments among branches) does not guarantee non-redundancy (let alone minimality).…”

“…So, important tools for minimization are algorithms for testing containments and equivalences among queries [6,8,10,12]. We explore the notions of redundancy, minimization and the connection between them in a fragment of XPath that has been widely studied [4][5][6]13]. This fragment, XP {//,[ ], * } , consists of tree patterns with child and descendant edges, branches, and wildcards.…”

“…There is a claim [4] that every non-redundant pattern of XP {//,[ ], * } is also minimal. However, we show that the proof is incorrect.…”

“…Hence, the algorithm of [4] (which tests containments among branches) does not guarantee non-redundancy (let alone minimality).…”

“…Still, the approach of [4] is interesting because it attempts to characterize non-redundancy in terms of a local property, namely, whether there is a containment between a pair of branches that emanate from the same node. In comparison, the obvious characterization of non-redundancy is a global one, that is, there is no redundant node.…”