Modern Lower Bound Techniques in Database Theory and Constraint Satisfaction

TL;DR

This paper reviews various conditional lower bound techniques and their application to establishing the optimality of algorithms in database theory and constraint satisfaction problems.

Contribution

It provides an overview of different lower bound methods and demonstrates their application to problems in database theory and constraint satisfaction.

Findings

Conditional lower bounds can indicate the optimality of current algorithms.

Lower bounds based on ETH and P≠NP are applicable to database and constraint problems.

The tutorial clarifies how to apply lower bounds to real-world computational problems.

Abstract

Conditional lower bounds based on $P\neq NP$, the Exponential-Time Hypothesis (ETH), or similar complexity assumptions can provide very useful information about what type of algorithms are likely to be possible. Ideally, such lower bounds would be able to demonstrate that the best known algorithms are essentially optimal and cannot be improved further. In this tutorial, we overview different types of lower bounds, and see how they can be applied to problems in database theory and constraint satisfaction.