Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Distributed Covering Algorithms   We present a time-optimal deterministic distributed algorithm for
approximating a minimum weight vertex cover in hypergraphs of rank $f$. This
problem is equivalent to the Minimum Weight Set Cover problem in which the
frequency of every element is bounded by $f$. The approximation factor of our
algorithm is $(f+\epsilon)$. Our algorithm runs in the CONGEST model and
requires $O(\log\Delta/ \log\log\Delta)$ rounds, for constants
$\epsilon\in(0,1]$ and $f\in N^+$. This is the first distributed algorithm for
this problem whose running time does not depend on the vertex weights nor the
number of vertices. For constant values of $f$ and $\epsilon$, our algorithm
improves over the $(f+\epsilon)$-approximation algorithm of KMW06 whose running
time is $O(\log \Delta + \log W)$, where $W$ is the ratio between the largest
and smallest vertex weights in the graph. Our algorithm also achieves an
$f$-approximation for the problem in $O(f\log n)$ rounds, improving over the
classical result of KVY94 that achieves a running time of $O(f\log^2 n)$.
Finally, for weighted vertex cover ($f=2$) our algorithm achieves a
\emph{deterministic} running time of $O(\log n)$, matching the
\emph{randomized} previously best result of KY11. We also show that integer
covering-programs can be reduced to the Minimum Weight Set Cover problem in the
distributed setting. This allows us to achieve an $(f+\epsilon)$-approximate
integral solution in $O(\frac{\log\Delta}{\log\log\Delta}+(f\cdot\log
M)^{1.01}\log\epsilon^{-1}(\log\Delta)^{0.01})$ rounds, where $f$ bounds the
number of variables in a constraint, $\Delta$ bounds the number of constraints
a variable appears in, and $M=\max \{1, 1/a_{\min}\}$, where $a_{min}$ is the
smallest normalized constraint coefficient. This improves over the results of
KMW06 for the integral case, which runs in $O(\epsilon^{-4}\cdot f^4\cdot \log
f\cdot\log(M\cdot\Delta))$ rounds.

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The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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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: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph