Assuming the Exponential Time Hypothesis (ETH), a result of Marx (ToC'10) implies that there is no f(k)⋅no(k/logk) time algorithm that can solve 2-CSPs with k constraints (over a domain of arbitrary large size n) for any computable function f. This lower bound is widely used to show that certain parameterized problems cannot be solved in time f(k)⋅no(k/logk) time (assuming the ETH). The purpose of this note is to give a streamlined proof of this result.
@article{arxiv.2311.05913,
title = {Conditional lower bounds for sparse parameterized 2-CSP: A streamlined proof},
author = {Karthik C. S. and Dániel Marx and Marcin Pilipczuk and Uéverton Souza},
journal= {arXiv preprint arXiv:2311.05913},
year = {2024}
}