Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Algorithms Optimally Recover (Censored) Planted Dense Subgraphs   We study spectral algorithms for the planted dense subgraph problem (PDS), as
well as for a censored variant (CPDS) of PDS, where the edge statuses are
missing at random. More precisely, in the PDS model, we consider $n$ vertices
and a random subset of vertices $S^{\star}$ of size $\Omega(n)$, such that two
vertices share an edge with probability $p$ if both of them are in $S^{\star}$,
and all other edges are present with probability $q$, independently. The goal
is to recover $S^{\star}$ from one observation of the network. In the CPDS
model, edge statuses are revealed with probability $\frac{t \log n}{n}$. For
the PDS model, we show that a simple spectral algorithm based on the top two
eigenvectors of the adjacency matrix can recover $S^{\star}$ up to the
information theoretic threshold. Prior work by Hajek, Wu and Xu required a less
efficient SDP based algorithm to recover $S^{\star}$ up to the information
theoretic threshold. For the CDPS model, we obtain the information theoretic
limit for the recovery problem, and further show that a spectral algorithm
based on a special matrix called the signed adjacency matrix recovers
$S^{\star}$ up to the information theoretic threshold.

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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
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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: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th