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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 cansolve 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 thatcertain parameterized problems cannot be solved in time $f(k)\cdot n^{o(k/\logk)}$ time (assuming the ETH). The purpose of this note is to give a streamlinedproof of this result.

Conditional lower bounds for sparse parameterized 2-CSP: A streamlined proof