On independent sets, 2-to-2 games, and Grassmann graphs

@article{Khot2016OnIS,
  title={On independent sets, 2-to-2 games, and Grassmann graphs},
  author={Subhash Khot and Dor Minzer and Shmuel Safra},
  journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2016}
}
  • Subhash Khot, Dor Minzer, S. Safra
  • Published 19 June 2017
  • Computer Science, Mathematics
  • Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
We present a candidate reduction from the 3-Lin problem to the 2-to-2 Games problem and present a combinatorial hypothesis about Grassmann graphs which, if correct, is sufficient to show the soundness of the reduction in a certain non-standard sense. A reduction that is sound in this non-standard sense implies that it is NP-hard to distinguish whether an n-vertex graph has an independent set of size ( 1- 1/√2 ) n - o(n) or whether every independent set has size o(n), and consequently, that it… 
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