Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lexicographic products and the power of non-linear network coding   We introduce a technique for establishing and amplifying gaps between
parameters of network coding and index coding. The technique uses linear
programs to establish separations between combinatorial and coding-theoretic
parameters and applies hypergraph lexicographic products to amplify these
separations. This entails combining the dual solutions of the lexicographic
multiplicands and proving that they are a valid dual of the product. Our result
is general enough to apply to a large family of linear programs. This blend of
linear programs and lexicographic products gives a recipe for constructing hard
instances in which the gap between combinatorial or coding-theoretic parameters
is polynomially large. We find polynomial gaps in cases in which the largest
previously known gaps were only small constant factors or entirely unknown.
Most notably, we show a polynomial separation between linear and non-linear
network coding rates. This involves exploiting a connection between matroids
and index coding to establish a previously unknown separation between linear
and non-linear index coding rates. We also construct index coding problems with
a polynomial gap between the broadcast rate and the trivial lower bound for
which no gap was previously known.

30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int