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：假设指数时间假说（ETH），Marx（ToC'10）的一个结果表明，不存在任何可计算函数$f$使得算法能够在$f(k)\cdot n^{o(k/\log k)}$时间内求解包含$k$个约束（定义域大小$n$可任意大）的2-CSP问题。该下界被广泛用于证明某些参数化问题在ETH假设下无法在$f(k)\cdot n^{o(k/\log k)}$时间内求解。本文旨在给出该结果的一个简洁证明。