Conjunctive Queries with Negation and Aggregation: A Linear Time Characterization

TL;DR

This paper characterizes the linear-time evaluation of certain conjunctive queries with negation and aggregation, introducing efficient algorithms for specific classes and exploring their limitations and applications.

Contribution

It provides a linear-time algorithm for free-connex signed-acyclic queries with negation and extends it to aggregate queries over semirings, revealing complexity bounds and structural conditions.

Findings

Linear preprocessing and constant delay enumeration for free-connex signed-acyclic queries.

Introduction of an algorithm for aggregate queries with a preprocessing time involving inverse Ackermann function.

Application of results to efficiently compute the difference of conjunctive queries.

Abstract

In this paper, we study the complexity of evaluating Conjunctive Queries with negation (\cqneg). First, we present an algorithm with linear preprocessing time and constant delay enumeration for a class of CQs with negation called free-connex signed-acyclic queries. We show that no other queries admit such an algorithm subject to lower bound conjectures. Second, we extend our algorithm to Conjunctive Queries with negation and aggregation over a general semiring, which we call Functional Aggregate Queries with negation (\faqneg). Such an algorithm achieves constant delay enumeration for the same class of queries, but with a slightly increased preprocessing time which includes an inverse Ackermann function. We show that this surprising appearance of the Ackermmann function is probably unavoidable for general semirings, but can be removed when the semiring has specific structure. Finally, we show an application of our results to computing the difference of CQs.