We present randomized distributed algorithms for the maximal independent set problem (MIS) that, while keeping the time complexity nearly matching the best known, reduce the energy complexity substantially. These algorithms work in the standard CONGEST model of distributed message passing with $O(\log n)$ bit messages. The time complexity measures the number of rounds in the algorithm. The energy complexity measures the number of rounds each node is awake; during other rounds, the node sleeps and cannot perform any computation or communications. Our first algorithm has an energy complexity of $O(\log\log n)$ and a time complexity of $O(\log^2 n)$. Our second algorithm is faster but slightly less energy-efficient: it achieves an energy complexity of $O(\log^2 \log n)$ and a time complexity of $O(\log n \cdot \log\log n \cdot \log^* n)$. Thus, this algorithm nearly matches the $O(\log n)$ time complexity of the state-of-the-art MIS algorithms while significantly reducing their energy complexity from $O(\log n)$ to $O(\log^2 \log n)$.

翻译：针对最大独立集问题（MIS），我们提出了随机分布式算法。这些算法在保持时间复杂度与当前最优方法几乎匹配的同时，显著降低了能量复杂度。算法运行在标准CONGEST分布式消息传递模型下，每条消息包含$O(\log n)$比特。时间复杂度衡量算法所需的轮数，能量复杂度则衡量每个节点处于活跃状态的轮数；在其余轮次中，节点休眠且无法执行任何计算或通信。我们的第一个算法实现了$O(\log \log n)$的能量复杂度和$O(\log^2 n)$的时间复杂度。第二个算法速度更快但能量效率略低：其能量复杂度为$O(\log^2 \log n)$，时间复杂度为$O(\log n \cdot \log \log n \cdot \log^* n)$。该算法的时间复杂度几乎与最优MIS算法的$O(\log n)$相匹配，同时将其能量复杂度从$O(\log n)$显著降低至$O(\log^2 \log n)$。