# Approximation resistance from pairwise independent subgroups

@article{Chan2013ApproximationRF,
title={Approximation resistance from pairwise independent subgroups},
author={Siu On Chan},
journal={Electron. Colloquium Comput. Complex.},
year={2013},
volume={19},
pages={110}
}
• S. Chan
• Published 1 June 2013
• Mathematics, Computer Science
• Electron. Colloquium Comput. Complex.
We show optimal (up to constant factor) NP-hardness for Max-k-CSP over any domain, whenever k is larger than the domain size. This follows from our main result concerning predicates over abelian groups. We show that a predicate is approximation resistant if it contains a subgroup that is balanced pairwise independent. This gives an unconditional analogue of Austrin--Mossel hardness result, bypassing the Unique-Games Conjecture for predicates with an abelian subgroup structure. Our main…
121 Citations

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