Coloring Fast Without Learning Your Neighbors' Colors

TL;DR

This paper presents an improved randomized distributed algorithm for distance-2 coloring in the CONGEST model, reducing the number of rounds needed and enhancing efficiency over previous methods.

Contribution

It introduces a faster algorithm for distance-2 coloring with fewer rounds, improving upon the previous state-of-the-art in distributed graph coloring.

Findings

Achieves $O(rac{ ext{log} }{ ext{log} ext{n}})$ round complexity.

Uses $ ext{Δ}^2+1$ colors for distance-2 coloring.

Significantly reduces the time complexity compared to prior algorithms.

Abstract

We give an improved randomized CONGEST algorithm for distance-$2$ coloring that uses $\Delta^2+1$ colors and runs in $O(\log n)$ rounds, improving the recent $O(\log \Delta \cdot \log n)$-round algorithm in [Halld\'orsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$.