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arXiv · 1603.01486

Distributed $(\Delta+1)$-Coloring in Sublogarithmic Rounds

David G. Harris·Johannes Schneider·Hsin-Hao Su
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Abstract

We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the $(\Delta+1)$-coloring problem is easier than the maximal independent set problem and the maximal matching problem, due to their lower bounds of $\Omega \left( \min \left( \sqrt{\frac{\log n}{\log \log n}}, \frac{\log \Delta}{\log \log \Delta} \right) \right)$ by Kuhn, Moscibroda, and Wattenhofer [PODC'04]. Our algorithm also extends to list-coloring where the palette of each node contains $\Delta+1$ colors. We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.

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David G. Harris, Johannes Schneider, Hsin-Hao Su. 2016-03-04. Distributed $(\Delta+1)$-Coloring in Sublogarithmic Rounds. https://arxiv.org/abs/1603.01486

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