Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Local Perspective on the Edge Removal Problem   The edge removal problem studies the loss in network coding rates that
results when a network communication edge is removed from a given network. It
is known, for example, that in networks restricted to linear coding schemes and
networks restricted to Abelian group codes, removing an edge e* with capacity
Re* reduces the achievable rate on each source by no more than Re*. In this
work, we seek to uncover larger families of encoding functions for which the
edge removal statement holds. We take a local perspective: instead of requiring
that all network encoding functions satisfy certain restrictions (e.g.,
linearity), we limit only the function carried on the removed edge e*. Our
central results give sufficient conditions on the function carried by edge e*
in the code used to achieve a particular rate vector under which we can
demonstrate the achievability of a related rate vector once e* is removed.

27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph