Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed $(\Delta+1)$-Coloring in Sublogarithmic Rounds   We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in
the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$
rounds in a graph of maximum degree~$\Delta$. This implies that the
$(\Delta+1)$-coloring problem is easier than the maximal independent set
problem and the maximal matching problem, due to their lower bounds of $\Omega
\left( \min \left( \sqrt{\frac{\log n}{\log \log n}}, \frac{\log \Delta}{\log
\log \Delta} \right) \right)$ by Kuhn, Moscibroda, and Wattenhofer [PODC'04].
Our algorithm also extends to list-coloring where the palette of each node
contains $\Delta+1$ colors. We extend the set of distributed symmetry-breaking
techniques by performing a decomposition of graphs into dense and sparse parts.

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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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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: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc