Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the k-pairs problem   We consider network coding rates for directed and undirected $k$-pairs
networks. For directed networks, meagerness is known to be an upper bound on
network coding rates. We show that network coding rate can be $\Theta(|V|)$
multiplicative factor smaller than meagerness. For the undirected case, we show
some progress in the direction of the $k$-pairs conjecture.

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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org