Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a Canonical Labeling Algorithm for the Alignment of
  Correlated Erd\H{o}s-R\'enyi Graphs   Graph alignment in two correlated random graphs refers to the task of
identifying the correspondence between vertex sets of the graphs. Recent
results have characterized the exact information-theoretic threshold for graph
alignment in correlated Erd\H{o}s-R\'enyi graphs. However, very little is known
about the existence of efficient algorithms to achieve graph alignment without
seeds.
  In this work we identify a region in which a straightforward $O(n^{11/5} \log
n )$-time canonical labeling algorithm, initially introduced in the context of
graph isomorphism, succeeds in aligning correlated Erd\H{o}s-R\'enyi graphs.
The algorithm has two steps. In the first step, all vertices are labeled by
their degrees and a trivial minimum distance alignment (i.e., sorting vertices
according to their degrees) matches a fixed number of highest degree vertices
in the two graphs. Having identified this subset of vertices, the remaining
vertices are matched using a alignment algorithm for bipartite graphs.

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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci