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

@article{Khot2016OnIS,
  title={On independent sets, 2-to-2 games, and Grassmann graphs},
  author={S. Khot and Dor Minzer and S. Safra},
  journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing},
  year={2016}
}
  • S. Khot, Dor Minzer, S. Safra
  • Published 2016
  • Mathematics, Computer Science
  • 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… CONTINUE READING
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    References

    SHOWING 1-8 OF 8 REFERENCES
    Some optimal inapproximability results
    • 1,669
    • Highly Influential
    • PDF
    A Parallel Repetition Theorem
    • R. Raz
    • Mathematics, Computer Science
    • SIAM J. Comput.
    • 1998
    • 194
    • Highly Influential
    Parallel Repetition in Projection Games and a Concentration Bound
    • A. Rao
    • Mathematics, Computer Science
    • SIAM J. Comput.
    • 2011
    • 14
    • Highly Influential
    Analytical approach to parallel repetition
    • 307
    • Highly Influential
    • PDF
    Proof verification and the hardness of approximation problems
    • 1,059
    • Highly Influential
    • PDF
    Parallel repetition: simplifications and the no-signaling case
    • 166
    • Highly Influential
    • PDF
    On the hardness of approximating minimum vertex cover
    • 572
    • Highly Influential
    • PDF
    Clique is hard to approximate withinn1−ε
    • 1,045
    • Highly Influential