Information about Queries Obtained by a Set of Views

Significant research has been done on examining the problems of generating equivalent rewritings (ER) or maximally-contained rewritings (MCR) of queries. At the same time, when ERs and MCRs do not exist, users can still use views to obtain meaningful information on their queries. Emerging applications require a study of the problem of rewriting queries using views in a variety of new scenarios. For example, in web-search applications when MCRs may not exist, users may want to obtain a rewriting that provides all query answers (but may contain false positives). Even when an MCR is not available, security requirements of other applications may require checking whether any rewriting exists for a query using a set of views expressed in the fixed query language in which users can pose queries. In this paper we study contained and containing rewritings of a query using a set of views; the rewritings give a subset and a superset, respectively, of the query answer. We consider queries and views in the language of conjunctive queries with arithmetic comparisons (CQAC queries), and rewritings in the language of unions of CQAC queries. To the best of our knowledge, no algorithm is known for checking for the existence of MCRs for many interesting cases of CQAC queries and views. In those cases, our results can be used to compute some answers to a query using views — depending on the application — even if some other answers are missing or if false positives are obtained. We refer to a containing rewriting that contains no false negatives and with the minimal number of false positives (when using a given set of views) as a “minimally containing rewriting” (MiCR). While the running time of our algorithm for finding MiCRs is worst-case exponential in the size of the problem inputs, the algorithm performs well in many practical cases, due to its extensive pruning of the search space. Our experiments show good scalability of our algorithm.