Containment of Nested XML Queries

Query containment is the most fundamental relationship between a pair of database queries: a query Q is said to be contained in a query Q if the answer for Q is always a subset of the answer for Q, independent of the current state of the database. Query containment is an important problem in a wide variety of data management applications, including verification of integrity constraints, reasoning about contents of data sources in data integration, semantic caching, verification of knowledge bases, determining queries independent of updates, and most recently, in query reformulation for peer data management systems. Query containment has been studied extensively in the relational context and for XPath queries, but not for XML queries with nesting. We consider the theoretical aspects of the problem of query containment for XML queries with nesting. We begin by considering conjunctive XML queries (c-XQueries), and show that containment is in polynomial time if we restrict the fanout (number of sibling sub-blocks) to be 1. We prove that for arbitrary fanout, containment is coNP-hard already for queries with nesting depth 2, even if the query does not include variables in the return clauses. We then show that for queries with fixed nesting depth, containment is coNP-complete. Next, we establish the computational complexity of query containment for several practical extensions of c-XQueries, including queries with union and arithmetic comparisons, and queries where the XPath expressions may include descendant edges and negation. Finally, we describe a few heuristics for speeding up query containment checking in pracPermission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment. Proceedings of the 30th VLDB Conference, Toronto, Canada, 2004 tice by exploiting properties of the queries and the underlying schema.