Incremental view maintenance for XPath queries asks to maintain a materialized XPath view over an XML database. It assumes an underlying XML database D and a query Q. One is given a sequence of updates U to D, and the problem is to compute the result of Q(U(D)): the result of evaluating query Q on database D after having applied updates U. This article initiates a systematic study of the Boolean version of this problem. In the Boolean version, one only wants to know whether Q(U(D)) is empty or not.
In order to quickly answer this question, we are allowed to maintain an auxiliary data structure. The complexity of the maintenance algorithms is measured in, (1) the size of the auxiliary data structure, (2) the worst-case time per update needed to compute Q(U(D)), and (3) the worst-case time per update needed to bring the auxiliary data structure up to date. We allow three kinds of updates: node insertion, node deletion, and node relabeling. Our main results are that downward XPath queries can be incrementally maintained in time O(depth(D)·poly(|Q|)) per update and conjunctive forward XPath queries in time O(depth(D) · log(width(D))·poly(|Q|)) per update, where |Q| is the size of the query, and depth(D) and width(D) are the nesting depth and maximum number of siblings in database D, respectively. The auxiliary data structures for maintenance are linear in |D| and polynomial in |Q| in all these cases.