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arXiv · 1711.05469

Deterministic Distributed Edge-Coloring with Fewer Colors

Mohsen Ghaffari·Fabian Kuhn·Yannic Maus·Jara Uitto
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Abstract

We present a deterministic distributed algorithm, in the LOCAL model, that computes a $(1+o(1))Δ$-edge-coloring in polylogarithmic-time, so long as the maximum degree $Δ=\tildeΩ(\log n)$. For smaller $Δ$, we give a polylogarithmic-time $3Δ/2$-edge-coloring. These are the first deterministic algorithms to go below the natural barrier of $2Δ-1$ colors, and they improve significantly on the recent polylogarithmic-time $(2Δ-1)(1+o(1))$-edge-coloring of Ghaffari and Su [SODA'17] and the $(2Δ-1)$-edge-coloring of Fischer, Ghaffari, and Kuhn [FOCS'17], positively answering the main open question of the latter. The key technical ingredient of our algorithm is a simple and novel gradual packing of judiciously chosen near-maximum matchings, each of which becomes one of the color classes.

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Mohsen Ghaffari, Fabian Kuhn, Yannic Maus, Jara Uitto. 2017-11-15. Deterministic Distributed Edge-Coloring with Fewer Colors. https://arxiv.org/abs/1711.05469

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