Abstract
We give efficient randomized and deterministic distributed algorithms for computing a distance-$2$ vertex coloring of a graph $G$ in the CONGEST model. In particular, if $\Delta$ is the maximum degree of $G$, we show that there is a randomized CONGEST model algorithm to compute a distance-$2$ coloring of $G$ with $\Delta2+1$ colors in $O(\log\Delta\cdot\log n)$ rounds. Further if the number of colors is slightly increased to $(1+\epsilon)\Delta2$ for some $\epsilon>1/{\rm polylog}(n)$, we show that it is even possible to compute a distance-$2$ coloring deterministically in polylog$(n)$ time in the CONGEST model. Finally, we give a $O(\Delta2 + \log* n)$-round deterministic CONGEST algorithm to compute distance-$2$ coloring with $\Delta2+1$ colors.
We're not able to analyze this paper right now due to high demand.
Please check back later (sorry!).
Generate a summary of this paper on our Pro plan:
We ran into a problem analyzing this paper.