We obtain improved distributed algorithms in the CONGEST message-passing setting for problems on power graphs of an input graph $G$. This includes Coloring, Maximal Independent Set, and related problems. We develop a general deterministic technique that transforms R-round algorithms for $G$ with certain properties into $O(R \cdot \Delta^{k/2 - 1})$-round algorithms for $G^k$. This improves the previously-known running time for such transformation, which was $O(R \cdot \Delta^{k - 1})$. Consequently, for problems that can be solved by algorithms with the required properties and within polylogarithmic number of rounds, we obtain {quadratic} improvement for $G^k$ and {exponential} improvement for $G^2$. We also obtain significant improvements for problems with larger number of rounds in $G$.

翻译：我们在CONGEST消息传递模型下，针对输入图$G$的幂图上的问题获得了改进的分布式算法。这包括着色、极大独立集及相关问题。我们开发了一种通用的确定性技术，能将具有特定性质的$G$上的$R$轮算法转化为$G^k$上的$O(R \cdot \Delta^{k/2 - 1})$轮算法。这改进了此前已知的该转化运行时间$O(R \cdot \Delta^{k - 1})$。因此，对于可通过具有所需性质的算法在多项式对数轮数内解决的问题，我们在$G^k$上获得了{二次}改进，在$G^2$上获得了{指数}改进。对于$G$上需更多轮数的问题，我们也获得了显著改进。