# 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}
}
• Published in SIROCCO 2021
• Computer Science
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
2 Citations

#### Tables from this paper

Ultrafast Distributed Coloring of High Degree Graphs
• Computer Science
• ArXiv
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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
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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