Lower Bounds for Conjunctive Query Evaluation

TL;DR

This paper surveys the complexity landscape of conjunctive query evaluation across various models, highlighting how recent complexity hypotheses suggest that existing algorithms are near-optimal and cannot be significantly improved.

Contribution

It connects recent complexity theory hypotheses to query evaluation, providing insights into the optimality of current algorithms across multiple models.

Findings

Known algorithms are likely optimal under certain complexity hypotheses.

Connections between complexity hypotheses and query evaluation are established.

Survey covers Boolean, enumeration, and direct access models.

Abstract

In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus will be on showing how different relatively recent hypotheses from complexity theory connect to query answering and allow showing that known algorithms in several cases can likely not be improved.