All reports by Author Shuo Pang:

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TR21-070
| 13th May 2021
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Shuo Pang#### SOS lower bound for exact planted clique

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TR19-068
| 27th April 2019
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Shuo Pang#### LARGE CLIQUE IS HARD ON AVERAGE FOR RESOLUTION

Revisions: 1

Shuo Pang

We prove a SOS degree lower bound for the planted clique problem on Erd{\"o}s-R\'enyi random graphs $G(n,1/2)$. The bound we get is degree $d=\Omega(\epsilon^2\log n/\log\log n)$ for clique size $\omega=n^{1/2-\epsilon}$, which is almost tight. This improves the result of \cite{barak2019nearly} on the ``soft'' version of the problem, where the family ... more >>>

Shuo Pang

We prove resolution lower bounds for $k$-Clique on the Erdos-Renyi random graph $G(n,n^{-{2\xi}\over{k-1}})$ (where $\xi>1$ is constant). First we show for $k=n^{c_0}$, $c_0\in(0,1/3)$, an $\exp({\Omega(n^{(1-\epsilon)c_0})})$ average lower bound on resolution where $\epsilon$ is arbitrary constant.

We then propose the model of $a$-irregular resolution. Extended from regular resolution, this model ... more >>>