Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lecture Notes on the ARV Algorithm for Sparsest Cut   One of the landmarks in approximation algorithms is the $O(\sqrt{\log
n})$-approximation algorithm for the Uniform Sparsest Cut problem by Arora, Rao
and Vazirani from 2004. The algorithm is based on a semidefinite program that
finds an embedding of the nodes respecting the triangle inequality. Their core
argument shows that a random hyperplane approach will find two large sets of
$\Theta(n)$ many nodes each that have a distance of $\Theta(1/\sqrt{\log n})$
to each other if measured in terms of $\|\cdot \|_2^2$.
  Here we give a detailed set of lecture notes describing the algorithm. For
the proof of the Structure Theorem we use a cleaner argument based on expected
maxima over $k$-neighborhoods that significantly simplifies the analysis.

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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th