Aggregate Queries on Sparse Databases

Abstract: We propose an algebraic framework for studying efficient algorithms for query evaluation, aggregation, enumeration, and maintenance under updates, on sparse databases. Our framework allows to treat those problems in a unified way, by considering various semirings, depending on the considered problem. As a concrete application, we propose a powerful query language extending first-order logic by aggregation in multiple semirings. We obtain an optimal algorithm for computing the answers of such queries on sparse databases. More precisely, given a database from a fixed class with bounded expansion, the algorithm computes in linear time a data structure which allows to enumerate the set of answers to the query, with constant delay between two outputs.