Before revision:  The key ingredient is an \mathcal{O}(n \operatorname{polylog} n)-size factorized representation of the query output, which is constructed on-the-fly for a given query and database.
After revision:  The key ingredient is a novel \mathcal{O}(n \operatorname{polylog} n)-size factorized representation of the query output, which is constructed on-the-fly for a given query and database.