AI 中文总结
本文引入自稳定SLEEPING模型，提出能效算法求解三类分布式问题，并给出两种转换算法适配静默自稳定算法，以平衡三类复杂度指标降低能耗。
AI 中文摘要
SLEEPING LOCAL模型引入了新的复杂度参数——唤醒复杂度，以实现分布式算法的能效优化。在同步LOCAL模型中，节点可在每一轮选择处于唤醒或睡眠状态；每一轮中，仅唤醒节点可通信以共享信息，此过程会消耗能量。唤醒复杂度指节点被激活以产生输出的最大次数，与每轮所有节点均唤醒的算法相比，该参数通常会以增加问题求解所需总轮数为代价。本文将唤醒轮次的概念适配到自稳定场景中，引入自稳定SLEEPING模型，节点无需始终保持唤醒状态，但在自稳定场景中，节点必须被无限次激活以检测系统当前状态的任何问题。该模型需考量三类复杂度指标：达到合法配置所需的同步轮数、节点达到该配置所需的唤醒次数、达到配置后节点需保持唤醒的频率，目标是最小化这三个指标，且可预期存在不同的权衡关系。本文提出能效算法，用于求解(Δ+1)着色、最大独立集（Maximal Independent Set）和最大匹配（Maximal Matching）问题，方法是采用新的专用睡眠技术以降低收敛阶段的唤醒复杂度（即能耗）；还提出两种转换算法，将静默自稳定算法适配到SLEEPING设置：第一种转换算法较为简单，适用于低复杂度算法；第二种转换算法更复杂，在转换慢自稳定算法时能效更高。
英文摘要
The SLEEPING LOCAL model introduces a new complexity parameter, the awake complexity, to make distributed algorithms energy-efficient. In the synchronous LOCAL model, nodes can now decide to be awake or asleep in each round. In a round, only awake nodes can communicate to share information, which consumes energy. The awake complexity is the maximum number of times a node is activated to produce an output. In particular, it often comes at the cost of the total number of rounds required to solve a problem, compared with algorithms in which every node is awake in every round. In this article, we adapt the notion of awaken rounds to the context of self-stabilization, introducing the Self-Stabilizing SLEEPING model. Nodes are no longer required to remain awake at all times. However, in self-stabilization, nodes must be activated infinitely often to detect any issue in the system's current state. In this model, the complexities are: * How many synchronous rounds are needed to reach a legitimate configuration? * How many times does a node need to be awake to reach this configuration? * How often does a node need to be awake once this configuration is reached? The goal is to minimize those three metrics, and we can expect different trade-offs. We present energy-efficient algorithms to solve the problems of finding a $(Δ+1)$-coloring, a Maximal Independent Set, and a Maximal Matching, thanks to new ad hoc sleeping techniques that reduce the awake complexity (i.e., energy consumption) during the convergence phase. We also propose two transformers that adapt silent self-stabilizing algorithms to the SLEEPING setup. The first transformer is pretty simple and deals with low-complexity algorithms. The second is more elaborate and is more energy-efficient when it transforms slow self-stabilizing algorithms.
