Answering Aggregate Queries with Ordered Direct Access

The paper presents recent findings on the fine-grained complexity of conjunctive queries with aggregation. For common aggregate functions (e.g., min, max, sum), such a query can be phrased as an ordinary conjunctive query over a database annotated with a suitable commutative semiring. We investigate the ability to evaluate queries by constructing in log-linear time a data structure that provides logarithmic-time direct access to the answers, ordered by a lexicographic order of choice. Importantly, these complexity guarantees hold even if the result of the query is asymptotically larger than log-linear in the size of the input.