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The Projection Games Conjecture and the NP-Hardness of ln n-Approximating Set-Cover
2015
Theory of Computing
We establish a tight NP-hardness result for approximating the SET-COVER problem based on a strong PCP theorem. Our work implies that it is NP-hard to approximate SET-COVER on instances of size N to within (1 − α) ln N for arbitrarily small α > 0. Our reduction establishes a tight trade-off between the approximation accuracy α and the running time exp(N Ω(α) ) assuming SAT requires exponential time. The reduction is obtained by modifying Feige's reduction. The latter provides a lower bound of
doi:10.4086/toc.2015.v011a007
dblp:journals/toc/Moshkovitz15
fatcat:sg65cikhdre7vdecuqrsmmvjqi