Memory lower bounds for XPath evaluation over XML streams

We consider the XPath evaluation problem: Evaluate an XPath query Q on a streaming XML document D. We consider two versions of the problem: 1) Filtering Problem: Determine if there is a match for Q in D. 2) Node Selection Problem: Determine the set Q ( D ) of document nodes selected by Q. We consider Conjunctive XPath ( CXPath) queries that involve only the child and descendant axes. Let d denote the depth of D, and n denote the number of location steps in Q. Bar-Yossef et al. (2007, 2005) [6,7] presented lower bounds on the memory space required by any algorithm to solve these two problems. Their lower bounds apply to each query in a large subset of XPath, and are obtained (mostly) using nonrecursive ( Q , D ) . In this paper, we present larger lower bounds for a different class of queries (namely, CXPath queries with independent predicates), on recursive ( Q , D ) . One of our results is an Ω ( n ⋅ maxcands ( Q , D ) ) lower bound for the node selection problem, for a worst-case Q; maxcands ( Q , D ) is the maximum number of nodes of D that can be candidates for output, at any one instant. So, there is no algorithm for the node selection problem that uses O ( f ( d , | Q | ) + maxcands ( Q , D ) ) space, for any function f. This shows that some previously published algorithms are incorrect.