Enumerating answers to first-order queries over databases of low degree

Abstract

A class of relational databases has low degree if for all δ, all but finitely many databases in the class have degree at most nδ, where n is the size of the database. Typical examples are databases of bounded degree or of degree bounded by log n. It is known that over a class of databases having low degree, first-order boolean queries can be checked in pseudo-linear time, i.e. in time bounded by n1+ε, for all ε. We generalise this result by considering query evaluation. We show that counting the number of answers to a query can be done in pseudo-linear time and that enumerating the answers to a query can be done with constant delay after a pseudo-linear time preprocessing.