Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Polynomial-Time Algorithm for Pliable Index Coding   In pliable index coding, we consider a server with $m$ messages and $n$
clients where each client has as side information a subset of the messages. We
seek to minimize the number of broadcast transmissions, so that each client can
recover any one unknown message she does not already have. Previous work has
shown that the pliable index coding problem is NP-hard and requires at most
$\mathcal{O}(\log^2(n))$ broadcast transmissions, which indicates exponential
savings over the conventional index coding that requires in the worst case
$\mathcal{O}(n)$ transmissions. In this work, building on a decoding criterion
that we propose, we first design a deterministic polynomial-time algorithm that
can realize the exponential benefits, by achieving, in the worst case, a
performance upper bounded by $\mathcal{O}(\log^2(n))$ broadcast transmissions.
We extend our algorithm to the $t$-requests case, where each client requires
$t$ unknown messages that she does not have, and show that our algorithm
requires at most $\mathcal{O}(t\log(n)+\log^2(n))$ broadcast transmissions. We
construct lower bound instances that require at least $\Omega(\log(n))$
transmissions for linear pliable index coding and at least $\Omega(t+\log(n))$
transmissions for the $t$-requests case, indicating that both our upper and
lower bounds are polynomials of $\log(n)$ and differ within a factor of
$\mathcal{O}(\log(n))$. Finally, we provide a probabilistic analysis and show
that the required number of transmissions is almost surely $\Theta(\log(n))$,
as compared to $\Theta(n/\log(n))$ for index coding. Our numerical experiments
show that our algorithm outperforms existing algorithms for pliable index
coding by up to $50\%$ less transmissions.

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The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th