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arXiv · 2105.04700

Ultrafast Distributed Coloring of High Degree Graphs

Magnús M. Halldórsson·Alexandre Nolin·Tigran Tonoyan
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Abstract

We give a new randomized distributed algorithm for the $\Delta+1$-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous refinements, and in particular, we can color all $n$-node graphs of maximum degree $\Delta \ge \log^{2+\Omega(1)} n$ in $O(\log^* n)$ rounds. The algorithm works in the CONGEST model, i.e., it uses only $O(\log n)$ bits per message for communication. On low-degree graphs, the algorithm shatters the graph into components of size $\operatorname{poly}(\log n)$ in $O(\log^* \Delta)$ rounds, showing that the randomized complexity of $\Delta+1$-list coloring in CONGEST depends inherently on the deterministic complexity of related coloring problems.

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Magnús M. Halldórsson, Alexandre Nolin, Tigran Tonoyan. 2021-05-10. Ultrafast Distributed Coloring of High Degree Graphs. https://arxiv.org/abs/2105.04700

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