Improved 3LIN Hardness via Linear Label Cover

Prahladh Harsha, Subhash Khot, Euiwoong Lee, Devanathan Thiruvenkatachari, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
We prove that for every constant c and ε = (log n) −c , there is no polynomial time algorithm that when given an instance of 3-LIN with n variables where an (1 − ε)-fraction of the clauses are satisfiable, finds an assignment that satisfies atleast ( 1 2 + ε)-fraction of clauses unless NP ⊆ BPP. The previous best hardness using a polynomial time reduction achieves ε = (log log n) −c , which is obtained by the Label Cover hardness of Moshkovitz and Raz [
doi:10.4230/lipics.approx-random.2019.9 dblp:conf/approx/HarshaKLT19 fatcat:vjy5cuwaqbambgcza7ev3gjlu4