Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Optimal Distributed $(\Delta+1)$-Coloring Algorithm?   Vertex coloring is one of the classic symmetry breaking problems studied in
distributed computing. In this paper we present a new algorithm for
$(\Delta+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in
$O(\mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$ time, where
$\mathsf{Det}_{\scriptscriptstyle d}(n')$ is the deterministic complexity of
$(\text{deg}+1)$-list coloring on $n'$-vertex graphs. (In this problem, each
$v$ has a palette of size $\text{deg}(v)+1$.) This improves upon a previous
randomized algorithm of Harris, Schneider, and Su [STOC'16, JACM'18] with
complexity $O(\sqrt{\log \Delta} + \log\log n +
\mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$, and, for some range
of $\Delta$, is much faster than the best known deterministic algorithm of
Fraigniaud, Heinrich, and Kosowski [FOCS'16] and Barenboim, Elkin, and
Goldenberg [PODC'18], with complexity $O(\sqrt{\Delta\log \Delta}\log^\ast
\Delta + \log^* n)$.
  Our algorithm "appears to be" optimal, in view of the
$\Omega(\mathsf{Det}(\text{poly} \log n))$ randomized lower bound due to Chang,
Kopelowitz, and Pettie [FOCS'16], where $\mathsf{Det}$ is the deterministic
complexity of $(\Delta+1)$-list coloring. At present, the best upper bounds on
$\mathsf{Det}_{\scriptscriptstyle d}(n')$ and $\mathsf{Det}(n')$ are both
$2^{O(\sqrt{\log n'})}$ and use a black box application of network
decompositions (Panconesi and Srinivasan [Journal of Algorithms'96]). It is
quite possible that the true complexities of both problems are the same,
asymptotically, which would imply the randomized optimality of our
$(\Delta+1)$-list coloring algorithm.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc