Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pliable Index Coding via Conflict-Free Colorings of Hypergraphs   In the pliable index coding (PICOD) problem, a server is to serve multiple
clients, each of which possesses a unique subset of the complete message set as
side information and requests a new message which it does not have. The goal of
the server is to do this using as few transmissions as possible. This work
presents a hypergraph coloring approach to the PICOD problem. A
\textit{conflict-free coloring} of a hypergraph is known from literature as an
assignment of colors to its vertices so that each edge of the graph contains
one uniquely colored vertex. For a given PICOD problem represented by a
hypergraph consisting of messages as vertices and request-sets as edges, we
present achievable PICOD schemes using conflict-free colorings of the PICOD
hypergraph. Various graph theoretic parameters arising out of such colorings
(and some new variants) then give a number of upper bounds on the optimal PICOD
length, which we study in this work. Our achievable schemes based on hypergraph
coloring include scalar as well as vector linear PICOD schemes. For the scalar
case, using the correspondence with conflict-free coloring, we show the
existence of an achievable scheme which has length $O(\log^2\Gamma),$ where
$\Gamma$ refers to a parameter of the hypergraph that captures the maximum
`incidence' number of other edges on any edge. This result improves upon known
achievability results in PICOD literature, in some parameter regimes.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio