论文标题
距离2中的距离-2颜色
Distance-2 Coloring in the CONGEST Model
论文作者
论文摘要
我们提供有效的随机和确定性分布式算法来计算距离$ 2 $ $ g $的顶点$ g $的距离。特别是，如果$δ$是$ g $的最高度，我们表明有一种随机的交货型算法来计算距离为$ 2 $ $ g $的$Δ^^2+1 $ $ o（\loguΔ\ cdot \ cdot \ log log n）$ n）的颜色。此外，如果对于某些$ε> 1/{\ rm polylog}（n）$的颜色数量略有增加到$（1+ε）δ^2 $，我们表明，甚至可以在会堂模型中以距离$ 2 $确定性地计算距离$ 2 $ 2 $。最后，我们给出了$ o（δ^2 + \ log^* n）$ - 圆形确定性拥塞算法来计算距离 - $ 2 $ coloring，用$δ^2 + 1 $颜色颜色。
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 $Δ$ 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 $Δ^2+1$ colors in $O(\logΔ\cdot\log n)$ rounds. Further if the number of colors is slightly increased to $(1+ε)Δ^2$ for some $ε>1/{\rm polylog}(n)$, 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 $O(Δ^2 + \log^* n)$-round deterministic CONGEST algorithm to compute distance-$2$ coloring with $Δ^2+1$ colors.
