# Superfast Coloring in CONGEST via Efficient Color Sampling

@inproceedings{Halldorsson2021SuperfastCI, title={Superfast Coloring in CONGEST via Efficient Color Sampling}, author={Magn'us M. Halld'orsson and Alexandre Nolin}, booktitle={SIROCCO}, year={2021} }

We present a procedure for efficiently sampling colors in the CONGEST model. It allows nodes whose number of colors exceeds their number of neighbors by a constant fraction to sample up to Θ(logn) semi-random colors unused by their neighbors in O(1) rounds, even in the distance-2 setting. This yields algorithms with O(log∗ ∆) complexity for different edge-coloring, vertex coloring, and distance-2 coloring problems, matching the best possible. In particular, we obtain an O(log∗ ∆)-round CONGEST… Expand

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Ultrafast Distributed Coloring of High Degree Graphs

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A new randomized distributed algorithm that can color all n-node graphs of maximum degree ∆ ≥ log n in O(log∗ n) rounds and shows that the randomized complexity of ∆ + 1-list coloring in Congest depends inherently on the deterministic complexity of related coloring problems. Expand

Distributed Graph Coloring Made Easy

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A deterministic CONGEST algorithm to compute an O(kΔ)-vertex coloring in O( Δ/k)+łog^* n rounds, where Δ is the maximum degree of the network graph and 1łeq kłeq O(Δ) can be freely chosen. Expand

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