On tree pattern query rewriting using views

We study and present our findings on two closely related problems on XPATH rewriting using views when both the view and the query are tree patterns involving /,// and []. First, given view V and query Q, is it possible for Q to have an equivalent rewriting using V which is the union of two or more tree patterns, but not an equivalent rewriting which is a single pattern? This problem is of both theoretical and practical importance because, if the answer is no, then, to answer a query completely using the views, we should use more efficient methods, such as the PTIME algorithm of [13], to find the equivalent rewriting, rather than try to find the union of all contained rewritings and test its equivalence to Q. Second, given a set V of views, we want to know under what conditions a subset V' of the views are redundant in the sense that for any query Q, the contained rewritings of Q using the views in V' are contained in those using the views in V-V'. Solving this problem can help us to, for example, choose the minimum number of views to be cached, or better design the virtual schema in a mediated data integration system, or avoid repeated calculation in query optimization. We provide necessary and sufficient conditions for the second problem, based on answers to the first problem. When the views produce comparable answers, we extend our findings to include the case where the intersection of views, in addition to the individual views, are used in the rewriting