Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder

@article{Austrin2019GlobalCC,
  title={Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder},
  author={Per Austrin and Aleksa Stankovic},
  journal={ArXiv},
  year={2019},
  volume={abs/1907.04165}
}
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal. In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within \approx 0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within \approx 0.929. In both cases, the previous best hardness results were the same as the hardness of the corresponding unconstrained Max-2-CSP (\approx… 

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