# A new point of NP-hardness for unique games

@inproceedings{ODonnell2012ANP, title={A new point of NP-hardness for unique games}, author={Ryan O'Donnell and John Wright}, booktitle={STOC '12}, year={2012} }

We show that distinguishing 1/2-satisfiable Unique-Games instances from (3/8 + ε)-satisfiable instances is NP-hard (for all ε > 0). A consequence is that we match or improve the best known c vs. s NP-hardness result for Unique-Games for all values of c (except for c very close to 0). For these c, ours is the first hardness result showing that it helps to take the alphabet size larger than 2. Our NP-hardness reductions are quasilinear-size and thus show nearly full exponential time is required… Expand

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