On the approximation resistance of balanced linear threshold functions

@article{Potechin2019OnTA,
  title={On the approximation resistance of balanced linear threshold functions},
  author={Aaron Potechin},
  journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing},
  year={2019}
}
  • Aaron Potechin
  • Published 12 July 2018
  • Mathematics
  • Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
In this paper, we show that there exists a balanced linear threshold function (LTF) which is unique games hard to approximate, refuting a conjecture of Austrin, Benabbas, and Magen. We also show that the almost monarchy predicate P(x) = sign((k−4)x1 + ∑i=2kxi) is approximable for sufficiently large k. 
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