Abstract. In this paper we address the problem of efficiently evaluating containment (i.e., subset, equality, and superset) queries over set-valued data. We propose a novel indexing scheme, the Ordered Inverted File (OIF) which, differently from the state-of-the-art, indexes set-valued attributes in an ordered fashion. We introduce query processing algorithms that practically treat containment queries as range queries over the ordered postings lists of OIF and exploit this ordering to quickly prune unnecessary page accesses. OIF is simple to implement and our experiments on both real and synthetic data show that it greatly outperforms the current state-of-the-art methods for all three classes of containment queries.