Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Does robustness imply tractability? A lower bound for planted clique in
  the semi-random model   We consider a robust analog of the planted clique problem. In this analog, a
set $S$ of vertices is chosen and all edges in $S$ are included; then, edges
between $S$ and the rest of the graph are included with probability
$\frac{1}{2}$, while edges not touching $S$ are allowed to vary arbitrarily.
For this semi-random model, we show that the information-theoretic threshold
for recovery is $\tilde{\Theta}(\sqrt{n})$, in sharp contrast to the classical
information-theoretic threshold of $\Theta(\log(n))$. This matches the
conjectured computational threshold for the classical planted clique problem,
and thus raises the intriguing possibility that, once we require robustness,
there is no computational-statistical gap for planted clique. Our lower bound
involves establishing a result regarding the KL divergence of a family of
perturbed Bernoulli distributions, which may be of independent interest.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th