Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Randomized Distributed Coloring in CONGEST   Distributed vertex coloring is one of the classic problems and probably also
the most widely studied problems in the area of distributed graph algorithms.
We present a new randomized distributed vertex coloring algorithm for the
standard CONGEST model, where the network is modeled as an $n$-node graph $G$,
and where the nodes of $G$ operate in synchronous communication rounds in which
they can exchange $O(\log n)$-bit messages over all the edges of $G$. For
graphs with maximum degree $\Delta$, we show that the $(\Delta+1)$-list
coloring problem (and therefore also the standard $(\Delta+1)$-coloring
problem) can be solved in $O(\log^5\log n)$ rounds. Previously such a result
was only known for the significantly more powerful LOCAL model, where in each
round, neighboring nodes can exchange messages of arbitrary size. The best
previous $(\Delta+1)$-coloring algorithm in the CONGEST model had a running
time of $O(\log\Delta + \log^6\log n)$ rounds. As a function of $n$ alone, the
best previous algorithm therefore had a round complexity of $O(\log n)$, which
is a bound that can also be achieved by a na\"{i}ve folklore algorithm. For
large maximum degree $\Delta$, our algorithm hence is an exponential
improvement over the previous state of the art.

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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: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
2
The categories of this paper are: math
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio