Sherali-Adams Strikes Back

@inproceedings{ODonnell2019SheraliAdamsSB,
  title={Sherali-Adams Strikes Back},
  author={R. O'Donnell and T. Schramm},
  booktitle={Computational Complexity Conference},
  year={2019}
}
  • R. O'Donnell, T. Schramm
  • Published in
    Computational Complexity…
    2019
  • Mathematics, Computer Science
  • Let $G$ be any $n$-vertex graph whose random walk matrix has its nontrivial eigenvalues bounded in magnitude by $1/\sqrt{\Delta}$ (for example, a random graph $G$ of average degree~$\Theta(\Delta)$ typically has this property). We show that the $\exp\Big(c \frac{\log n}{\log \Delta}\Big)$-round Sherali--Adams linear programming hierarchy certifies that the maximum cut in such a~$G$ is at most $50.1\%$ (in fact, at most $\tfrac12 + 2^{-\Omega(c)}$). For example, in random graphs with $n^{1.01… CONTINUE READING

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