Assuming the Exponential Time Hypothesis (ETH), a result of Marx (ToC'10) implies that there is no $f(k)\cdot n^{o(k/\log k)}$ 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 $f(k)\cdot n^{o(k/\log k)}$ time (assuming the ETH). The purpose of this note is to give a streamlined proof of this result.

翻译：假设指数时间假设（ETH），Marx（ToC'10）的一个结果蕴涵着：对于任意可计算函数$f$，不存在$f(k)\cdot n^{o(k/\log k)}$时间的算法能够求解具有$k个约束$（定义域规模$n$任意大）的2-CSP问题。该下界被广泛用于证明某些参数化问题不能在$f(k)\cdot n^{o(k/\log k)}$时间内求解（假设ETH成立）。本文旨在给出该结果的一个精简证明。