AI 中文总结
该研究提出基于信息论的通用技术，证明多个基础图问题的能量下界与轮下界匹配，无法获得显著能量增益。
AI 中文摘要
近期，在SLEEPING模型中设计最小化能量（即清醒）复杂度的分布式算法引起了显著关注，能量复杂度用于衡量节点在算法执行过程中处于清醒状态的轮数，节点仅在清醒而非睡眠状态下消耗大量资源（消息、能量等）。已有研究针对多个基础问题，围绕最小化节点清醒轮数的最坏情况或平均值展开能量复杂度分析，结果显示，领导者选举（LE）、广播、最小生成树（MST）、极大独立集（MIS）等多个基础问题的能量复杂度，相比标准CONGEST模型（节点仅能发送小尺寸消息）中各自最优的轮复杂度呈指数级降低。这引发了一个核心问题：其他众多基础问题是否也能实现如此显著的能量增益？本文的主要贡献是提出一种基于信息论的通用且强大的能量下界证明技术，该技术几乎可作为“即插即用”方法，用于证明标准CONGEST模型中各类问题的能量下界。借助该信息论技术，我们可利用已知的通信复杂度下界，推导得到三角形枚举、全对最短路径（APSP）、直径计算、最小权环、极大独立集（MaxIS）、最小支配集（MinDS）、最小顶点覆盖（MinVC）等基础图问题的新的、几乎最优（仅差对数因子）的多项式（与n相关）能量下界，涵盖最坏情况和平均情况。这些问题的能量下界与各自的轮下界相匹配，意味着无法在能量复杂度上获得任何显著增益。
英文摘要
There has been a significant recent interest in designing distributed algorithms in the SLEEPING model that minimize the {energy (a.k.a awake) complexity, which measures the number of rounds a node is awake during the algorithm. A node spends non-trivial resources (messages, energy, etc.) only when it is awake and not while sleeping. Energy complexity has been studied for various fundamental problems with respect to minimizing the maximum (worst-case) or the average number of rounds a node is awake. It has been shown that the energy complexities of several fundamental problems such as leader election (LE), broadcast, Minimum Spanning Tree (MST), Maximal Independent Set (MIS) is exponentially smaller compared to their respective best-possible round complexities in the standard CONGEST model (where nodes can only send messages of small size). This raises a fundamental question of whether such significant energy gains are possible for many other fundamental problems. Our main contribution is a general and powerful technique for showing energy lower bounds using information theory. It gives almost a "plug-in" way to show energy lower bounds for various problems in the standard CONGEST model. Our information-theoretic technique allows us to leverage known lower bounds on communication complexity to obtain new, almost optimal (up to logarithmic factors) polynomial (in $n$) lower bounds on energy complexity --- for both worst-case and average-case --- for fundamental graph problems such as triangle enumeration, All-Pairs Shortest Paths (APSP), diameter computation, minimum weight cycle, Maximum Independent Set (MaxIS), Minimum Dominating Set (MinDS), Minimum Vertex Cover (MinVC). The energy lower bounds of these problems match their respective round lower bounds, implying that one cannot obtain any significant gains in energy complexity.
CommentsTo appear at DISC 2026
