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arXiv · 2205.14478

Overcoming Congestion in Distributed Coloring

Magnús M. Halldórsson·Alexandre Nolin·Tigran Tonoyan
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Abstract

We present a new technique to efficiently sample and communicate a large number of elements from a distributed sampling space. When used in the context of a recent LOCAL algorithm for $(\operatorname{degree}+1)$-list-coloring (D1LC), this allows us to solve D1LC in $O(\log^5 \log n)$ CONGEST rounds, and in only $O(\log^* n)$ rounds when the graph has minimum degree $\Omega(\log^7 n)$, w.h.p. The technique also has immediate applications in testing some graph properties locally, and for estimating the sparsity/density of local subgraphs in $O(1)$ CONGEST rounds, w.h.p.

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Magnús M. Halldórsson, Alexandre Nolin, Tigran Tonoyan. 2022-05-28. Overcoming Congestion in Distributed Coloring. https://arxiv.org/abs/2205.14478

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