First-order queries on classes of structures with bounded expansion

TL;DR

This paper proves that first-order queries on classes of structures with bounded expansion can be evaluated efficiently, with linear-time preprocessing and constant delay enumeration, generalizing previous results for specific graph classes.

Contribution

It provides a new proof for linear-time evaluation of first-order queries and introduces enumeration with constant delay for classes with bounded expansion.

Findings

First-order query evaluation is linear in database size.

Enumeration of query answers can be done with constant delay.

Counting answers is achievable in linear time.

Abstract

We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It was known that over a class of databases with bounded expansion, first-order sentences could be evaluated in time linear in the size of the database. We give a different proof of this result. Moreover, we show that answers to first-order queries can be enumerated with constant delay after a linear time preprocessing. We also show that counting the number of answers to a query can be done in time linear in the size of the database.