Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seeded Graph Matching via Large Neighborhood Statistics   We study a well known noisy model of the graph isomorphism problem. In this
model, the goal is to perfectly recover the vertex correspondence between two
edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of
correctly matched vertex pairs revealed as side information. For seeded
problems, our result provides a significant improvement over previously known
results. We show that it is possible to achieve the information-theoretic limit
of graph sparsity in time polynomial in the number of vertices $n$. Moreover,
we show the number of seeds needed for exact recovery in polynomial-time can be
as low as $n^{3\epsilon}$ in the sparse graph regime (with the average degree
smaller than $n^{\epsilon}$) and $\Omega(\log n)$ in the dense graph regime.
  Our results also shed light on the unseeded problem. In particular, we give
sub-exponential time algorithms for sparse models and an $n^{O(\log n)}$
algorithm for dense models for some parameters, including some that are not
covered by recent results of Barak et al.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci