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

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