# Coloring Fast Without Learning Your Neighbors' Colors

@article{Halldrsson2020ColoringFW, title={Coloring Fast Without Learning Your Neighbors' Colors}, author={M. Halld{\'o}rsson and F. Kuhn and Yannic Maus and Alexandre Nolin}, journal={ArXiv}, year={2020}, volume={abs/2008.04303} }

We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\Delta^2+1$ colors and runs in $O(\log n)$ rounds, improving the recent $O(\log \Delta \cdot \log n)$-round algorithm in [Halldorsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$.

#### 3 Citations

Efficient CONGEST Algorithms for the Lovasz Local Lemma

- Computer Science
- ArXiv
- 2021

A poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs implies that there are no LCL problems with randomized complexity between log n and poly loglog n. Expand

Efficient randomized distributed coloring in CONGEST

- Mathematics, Computer Science
- STOC
- 2021

This work presents 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(logn)-bit messages over all the edges of G. Expand

Superfast Coloring in CONGEST via Efficient Color Sampling

- Computer Science
- SIROCCO
- 2021

An O(log∗ ∆)-round CONGEST algorithm for (2∆− 1)-edge coloring when ∆ ≥ log n, and poly(log logn)-round algorithm in general is obtained. Expand

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Coloring fast without learning your neighbors' colors

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